Reference documentation for deal.II version GIT relicensing-662-g00096bcf61 2024-05-18 15:40:02+00:00
\(\newcommand{\dealvcentcolon}{\mathrel{\mathop{:}}}\) \(\newcommand{\dealcoloneq}{\dealvcentcolon\mathrel{\mkern-1.2mu}=}\) \(\newcommand{\jump}[1]{\left[\!\left[ #1 \right]\!\right]}\) \(\newcommand{\average}[1]{\left\{\!\left\{ #1 \right\}\!\right\}}\)
No Matches

R. Agelek, M. Anderson, W. Bangerth, and W.L. Barth. On orienting edges of unstructured two- and three-dimensional meshes. ACM Transactions on Mathematical Software, 44(1):5/1–22, 2017.


M. Ainsworth and B. Senior. An adaptive refinement strategy for hp-finite element computations. Applied Numerical Mathematics, 26(1–2):165–178, 1998.


M. Ainsworth. A posteriori error estimation for discontinuous Galerkin finite element approximation. SIAM Journal on Numerical Analysis, 45(4):1777–1798, 2007.


P. Angot, C.-H. Bruneau, and P. Fabrie. A penalization method to take into account obstacles in incompressible viscous flows. Numerische Mathematik, 81(4):497–520, February 1999.


P. F. Antonietti, M. Sarti, M. Verani, and L. T. Zikatanov. A uniform additive Schwarz preconditioner for high-order discontinuous Galerkin approximations of elliptic problems. Journal of Scientific Computing, 70(2):608–630, 2016.


D. Arnold, F. Brezzi, B. Cockburn, and L. Marini. Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM Journal on Numerical Analysis, 39(5):1749–1779, 2002.


O. Axelsson, M. Neytcheva, and B. Ahmad. A comparison of iterative methods to solve complex valued linear algebraic systems. Numerical Algorithms, 66:811–841, 2014.


I. Babuska and J.M. Melenk. The partition of unity method. International Journal for Numerical Methods in Engineering, 40(4):727–758, 1997.


W. Bangerth and R. Rannacher. Finite element approximation of the acoustic wave equation: Error control and mesh adaptation. East–West Journal of Numerical Mathematics, 7(4):263–282, 1999.


W. Bangerth and R. Rannacher. Adaptive finite element techniques for the acoustic wave equation. Journal of Computational Acoustics, 9(2):575–591, 2001.


W. Bangerth and R. Rannacher. Adaptive Finite Element Methods for Differential Equations. Birkhäuser Verlag, 2003.


W. Bangerth, M. Geiger, and R. Rannacher. Adaptive Galerkin finite element methods for the wave equation. Computational Methods in Applied Mathematics, 10(1):3–48, 2010.


W. Bangerth. Mesh adaptivity and error control for a finite element approximation of the elastic wave equation. In Alfredo Bermúdez, Dolores Gómez, Christophe Hazard, Patrick Joly, and Jean E. Roberts, editors, Proceedings of the Fifth International Conference on Mathematical and Numerical Aspects of Wave Propagation (Waves2000), Santiago de Compostela, Spain, 2000, pages 725–729. SIAM, 2000.


W. Bangerth. Adaptive Finite Element Methods for the Identification of Distributed Parameters in Partial Differential Equations. PhD thesis, University of Heidelberg, 2002.


N.A. Barnafi, L.F. Pavarino, and S. Scacchi. A comparative study of scalable multilevel preconditioners for cardiac mechanics, 2022.


S. Bartels, C. Carstensen, and G. Dolzmann. Inhomogeneous dirichlet conditions in a priori and a posteriori finite element error analysis. Numerische Mathematik, 99(1):1–24, September 2004.


A. Battermann. Preconditioning of karush–kuhn–tucker systems arising in optimal control problems. Master's thesis, Virginia Tech, June 1996.


J. Bebernes and D. Eberly. Mathematical Problems from Combustion Theory, volume 83 of Applied Mathematical Sciences. Springer-Verlag, New York, NY, 1989.


R. Becker and R. Rannacher. A feed-back approach to error control in finite element methods: Basic analysis and examples. East–West Journal of Numerical Mathematics, 4:237–264, 1996.


R. Becker and R. Rannacher. Weighted a posteriori error control in FE methods. In H. G. Bock et al., editor, ENUMATH 97, pages 621–637. World Scientific Publishing, Singapore, 1998.


R. Becker and R. Rannacher. An optimal control approach to error estimation and mesh adaptation in finite element methods. Acta Numerica, 10:1–102, 2001.


R. Becker. An Adaptive Finite Element Method for the Incompressible Navier–Stokes Equations on Time-dependent Domains. PhD thesis, Universität Heidelberg, 1995.


R. Becker. Weighted error estimators for the incompressible Navier–Stokes equations. Preprint 98-20, Universität Heidelberg, 1998.


M.P. Bendsøe and O. Sigmund. Topology Optimization. Springer Berlin Heidelberg, 2004.


H.Y. Benson, R.J. Vanderbei, and D.F. Shanno. Interior-point methods for nonconvex nonlinear programs: Filter methods and merit functions. Computational Optimization and Applications, 23(2):257–272, 2002.


M. Benzi and M.A. Olshanskii. An augmented lagrangian‐based approach to the oseen problem. SIAM Journal on Scientific Computing, 28:2095–2113, 2006.


M. Bercovier and O. Pironneau. Error estimates for finite element method solution of the Stokes problem in the primitive variables. Numerische Mathematik, 33(2):211–224, June 1979.


J.-P. Bérenger. A perfectly matched layer for the absorption of electromagnetic waves. Journal of Computational Physics, 114:185–200, 1994.


Daniel Bielich, Julien Langou, Stephen Thomas, Kasia Świrydowicz, Ichitaro Yamazaki, and Erik G. Boman. Low-synch Gram–Schmidt with delayed reorthogonalization for Krylov solvers. Parallel Computing, 112:102940, 2022.


F. Black and M. Scholes. The pricing of options and corporate liabilities. The Journal of Political Economy, 81(3):637–654, 1973.


B. Blais, J.-P. Braeunig, D. Chauveheid, J.-M. Ghidaglia, and R. Loubère. Dealing with more than two materials in the FVCF–ENIP method. European Journal of Mechanics-B/Fluids, 42:1–9, 2013.


B. Blais, D. Vidal, F. Bertrand, G.S. Patience, and J. Chaouki. Experimental methods in chemical engineering: Discrete element method–DEM. The Canadian Journal of Chemical Engineering, 97(7):1964–1973, 2019.


D. Boffi, L. Gastaldi, L. Heltai, and Ch.S. Peskin. On the hyper-elastic formulation of the immersed boundary method. Computer Methods in Applied Mechanics and Engineering, 197(25-28):2210–2231, April 2008.


D. Boffi, N. Cavallini, F. Gardini, and L. Gastaldi. Local mass conservation of stokes finite elements. Journal of Scientific Computing, 52(2):383–400, November 2011.


D. Boffi, N. Cavallini, F. Gardini, and L. Gastaldi. Local mass conservation of stokes finite elements. Journal of Scientific Computing, 52:383–400, 2012.


A. Bonito, R.H. Nochetto, and D. Ntogkas. DG approach to large bending plate deformations with isometry constraint. Mathematical Models and Methods in Applied Sciences, 31(1):133–175, 2021.


A. Bonito, D. Guignard, R.H. Nochetto, and S. Yang. LDG approximation of large deformations of prestrained plates. Journal of Computational Physics, 448:110719/1–27, January 2022.


A. Bonito, D. Guignard, R.H. Nochetto, and S. Yang. Numerical analysis of the LDG method for large deformations of prestrained plates. IMA Journal of Numerical Analysis, 43(2):627–662, March 2022.


Jeremiah U Brackbill, Douglas B Kothe, and Charles Zemach. A continuum method for modeling surface tension. Journal of computational physics, 100(2):335–354, 1992.


S. Brenner and R. Scott. The Mathematical Theory of Finite Element Methods. Texts in Applied Mathematics. Springer-Verlag, 3 edition, 2008.


S.C. Brenner and L.-Y. Sung. C \(^0\) interior penalty methods for fourth order elliptic boundary value problems on polygonal domains. Journal of Scientific Computing, 22(1):83–118, June 2005.


S.C. Brenner, T. Gudi, and L.-Y. Sung. An a posteriori error estimator for a quadratic \(C^0\)-interior penalty method for the biharmonic problem. IMA Journal of Numerical Analysis, 30(3):777–798, March 2010.


S.C. Brenner. C \(^0\) interior penalty methods. In Lecture Notes in Computational Science and Engineering, pages 79–147. Springer Berlin Heidelberg, 2011.


F. Brezzi and M. Fortin. Mixed and Hybrid Finite Element Methods. Springer, 1991.


A.N. Brooks and T.J.R. Hughes. Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering, 32(1-3):199–259, 1982. FENOMECH ''81, Part I (Stuttgart, 1981).


C.-H. Bruneau and M. Saad. The 2d lid-driven cavity problem revisited. Computers & Fluids, 35:326–348, 2006.


S.E. Buckley and M.C. Leverett. Mechanism of fluid displacement in sands. Transactions of the AIME, 146(01):107–116, December 1942.


Hans-Joachim Bungartz, Florian Lindner, Bernhard Gatzhammer, Miriam Mehl, Klaudius Scheufele, Alexander Shukaev, and Benjamin Uekermann. preCICE – a fully parallel library for multi-physics surface coupling. Computers & Fluids, 141:250–258, 2016.


E. Burman and P. Hansbo. Fictitious domain finite element methods using cut elements: II. A stabilized Nitsche method. Applied Numerical Mathematics, 62(4):328–341, April 2012.


E. Burman, S. Claus, P. Hansbo, M.G. Larson, and A. Massing. CutFEM: Discretizing geometry and partial differential equations. International Journal for Numerical Methods in Engineering, 104(7):472–501, November 2015.


Erik Burman, Susanne Claus, Peter Hansbo, Mats G Larson, and André Massing. Cutfem: discretizing geometry and partial differential equations. International Journal for Numerical Methods in Engineering, 104(7):472–501, 2015.


A. Cangiani, J. Chapman, E.H. Georgoulis, and M. Jensen. Implementation of the continuous-discontinuous Galerkin finite element method. In Numerical Mathematics and Advanced Applications 2011, pages 315–322. Springer Berlin Heidelberg, November 2012.


G.F. Castelli. Numerical Investigation of Cahn–Hilliard-Type Phase-Field Models for Battery Active Particles. PhD thesis, Karlsruhe Institute of Technology (KIT), 2021.


Z. Chen. Finite Element Methods and their Applications. Springer, 2005.


Gerasimos Chourdakis, Kyle Davis, Benjamin Rodenberg, Miriam Schulte, Frédéric Simonis, Benjamin Uekermann, Georg Abrams, Hans-Joachim Bungartz, Lucia Cheung Yau, Ishaan Desai, and others. preCICE v2: A sustainable and user-friendly coupling library. arXiv preprint arXiv:2109.14470, 2021.


A. T. Chronopoulos and C. W. Gear. S-step iterative methods for symmetric linear systems. Journal of Computational and Applied Mathematics, 25(2):153–168, 1989.


C.C. Chueh, M. Secanell, W. Bangerth, and N. Djilali. Multi-level adaptive simulation of transient two-phase flow in heterogeneous porous media. Computers & Fluids, 39(9):1585–1596, 2010.


C.C. Chueh, N. Djilali, and W. Bangerth. An \(h\)-adaptive operator splitting method for two-phase flow in 3d heterogeneous porous media. SIAM Journal on Scientific Computing, 35(1):B149–B175, 2013.


P. Ciarlet and P. Raviart. General langrange and hermite interpolation in \(\mathbb{R}^{n}\) with applications to finite element methods. Archive for rational mechanics and analysis, 46:177–199, 1972.


T.C. Clevenger, T. Heister, G. Kanschat, and M. Kronbichler. A flexible, parallel, adaptive geometric multigrid method for FEM. ACM Transactions on Mathematical Software, 47(1):7/1–27, March 2021.


B. Cockburn, J. Gopalakrishnan, and R. Lazarov. Unified hybridization of discontinuous Galerkin, mixed, and continuous Galerkin methods for second order elliptic problems. SIAM Journal on Numerical Analysis, 47(2):1319–1365, 2009.


B.D. Coleman and M.E. Gurtin. Thermodynamics with internal state variables. The Journal of Chemical Physics, 47(2):597–613, 1967.


B.D. Coleman and W. Noll. The thermodynamics of elastic materials with heat conduction and viscosity. Archive for Rational Mechanics and Analysis, 13(1):167–178, 1963.


E. Comellas, J.-P. Pelteret, and W. Bangerth. I'm stuck! how to efficiently debug computational solid mechanics models so you can enjoy the beauty of simulations. European Journal of Mechanics - A/Solids, 97:104845, jan 2023.


S. Commend, A. Truty, and T. Zimmermann. Stabilized finite elements applied to elastoplasticity: I. Mixed displacement–pressure formulation. Computer Methods in Applied Mechanics and Engineering, 193(33):3559–3586, 2004.


Mathieu Coquerelle and Stéphane Glockner. A fourth-order accurate curvature computation in a level set framework for two-phase flows subjected to surface tension forces. Journal of Computational Physics, 305:838–876, 2016.


D. Davydov, T. Gerasimov, J.-P. Pelteret, and P. Steinmann. Convergence study of the h-adaptive PUM and the hp-adaptive FEM applied to eigenvalue problems in quantum mechanics. Advanced Modeling and Simulation in Engineering Sciences, 4(1):7, 2017.


D. Day and M.A. Heroux. Solving complex-valued linear systems via equivalent real formulations. SIAM Journal on Scientific Computing, 23:480–498, 2001.


B.X. Fraeijs de Veubeke. Displacement and equilibrium models in the finite element method. In O.C. Zienkiewicz and G.S. Holister, editors, Stress Analysis, pages 275–284. Wiley, New York, 1965.


J. E. Dennis and R. B. Schnabel. Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Society for Industrial and Applied Mathematics, 1996.


H.-Y. Duan and Q. Lin. Mixed finite elements of least-squares type for elasticity. Computer Methods in Applied Mechanics and Engineering, 194(9):1093–1112, 2005.


Jakob Dürrwächter, Marius Kurz, Patrick Kopper, Daniel Kempf, Claus-Dieter Munz, and Andrea Beck. An efficient sliding mesh interface method for high-order discontinuous Galerkin schemes. Computers & Fluids, 217:104825, mar 2021.


T. Eibner and J.M. Melenk. An adaptive strategy for hp-FEM based on testing for analyticity. Computational Mechanics, 39(5):575–595, 2007.


F.T. Eleuterio. Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer-Verlag, Berlin, Heidelberg, 2009.


H.C. Elman, D.J. Silvester, and A.J. Wathen. Finite Elements and Fast Iterative Solvers with Applications in Incompressible Fluid Dynamics. Numerical Mathematics and Scientific Computation. Oxford University Press, Oxford, New York, 2005.


G. Engel, K. Garikipati, T.J.R. Hughes, M.G. Larson, L. Mazzei, and R.L. Taylor. Continuous/discontinuous finite element approximations of fourth-order elliptic problems in structural and continuum mechanics with applications to thin beams and plates, and strain gradient elasticity. Computer Methods in Applied Mechanics and Engineering, 191(34):3669–3750, July 2002.


M. S. Engelman, R. L. Sani, and P. M. Gresho. The implementation of normal and/or tangential boundary conditions in finite element codes for incompressible fluid flow. Int. J. Numer. Meth. Fluids, 2:225–238, 1982.


A. Ern and J.-L. Guermond. Theory and practice of finite elements, volume 159 of Applied Mathematical Sciences. Springer-Verlag, New York, 2004.


E. Erturk, T.C. Corke, and C. Gökçöl. Numerical solutions of 2-d steady incompressible driven cavity flow at high reynolds numbers. International Journal for Numerical Methods in Fluids, 48:747–774, 2005.


M. Fehling. Algorithms for massively parallel generic hp-adaptive finite element methods. PhD thesis, Bergische Universität Wuppertal, 2020.


N. Fehn, W.A. Wall, and M. Kronbichler. A matrix-free high-order discontinuous Galerkin compressible Navier–Stokes solver: A performance comparison of compressible and incompressible formulations for turbulent incompressible flows. International Journal for Numerical Methods in Fluids, 89(3):71–102, 2019.


N. Fehn, P. Munch, W. A. Wall, and M. Kronbichler. Hybrid multigrid methods for high-order discontinuous Galerkin discretizations. Journal of Computational Physics, 415:109538, 2020.


M. Fowler. Refactoring: Improving the Design of Existing Code. Addison-Wesley, second edition, 2018.


V. Frayssé, L. Giraud, S. Gratton, and J. Langou. Algorithm 842: A set of gmres routines for real and complex arithmetics on high performance computers. ACM Transactions on Mathematical Software, 31:228–238, 2005.


J. Freund and R. Stenberg. On weakly imposed boundary conditions for second order problems. In Proceedings of the Ninth International Conference on Finite Elements in Fluids, pages 327–336, 1995.


I. Fried and D.S. Malkus. Finite element mass matrix lumping by numerical integration with no convergence rate loss. International Journal of Solids and Structures, 11(4):461–466, 1975.


C. Führer and G. Kanschat. A posteriori error control in radiative transfer. Computing, 58(4):317–334, 1997.


R. Gassmöller, H. Lokavarapu, E. Heien, E.G. Puckett, and W. Bangerth. Flexible and scalable particle-in-cell methods with adaptive mesh refinement for geodynamic computations. Geochemistry, Geophysics, Geosystems, 19(9):3596–3604, 2018.


R. Gassmöller, H. Lokavarapu, W. Bangerth, and E.G. Puckett. Evaluating the accuracy of hybrid finite element/particle-in-cell methods for modelling incompressible Stokes flow. Geophysical Journal International, 219(3):1915–1938, 2019.


G.J. Gassner. A skew-symmetric discontinuous Galerkin spectral element discretization and its relation to SBP-SAT finite difference methods. SIAM Journal on Scientific Computing, 35(3):A1233–A1253, 2013.


S. Geevers, W.A. Mulder, and J.J.W. van der Vegt. New higher-order mass-lumped tetrahedral elements for wave propagation modelling. SIAM Journal on Scientific Computing, 40(5):A2830–A2857, 2018.


U. Ghia, K.N. Ghia, and C.T. Shin. High-re solutions for incompressible flow using the navier-stokes equations and a multigrid method. Journal of Computational Physics, 48:387–411, 1982.


R. Glowinski, T.-W. Pan, T.I. Hesla, and D.D. Joseph. A distributed lagrange multiplier/fictitious domain method for particulate flows. International Journal of Multiphase Flow, 25(5):755–794, August 1999.


G.H. Golub and C.F. van Loan. Matrix Computations. Johns Hopkins, 1996.


J. Gopalakrishnan and J.E. Pasciak. Overlapping schwarz preconditioners for indefinite time harmonic Maxwell equations. Mathematics of Computation, 72:1–15, 2003.


S. Gottlieb, C.-W. Shu, and E. Tadmor. Strong stability-preserving high-order time discretization methods. SIAM review, 43(1):89–112, 2001.


I. Griva, S.G. Nash, and A. Sofer. Linear and nonlinear optimization. SIAM, 2nd edition, 2008.


J.-L. Guermond and R. Pasquetti. Entropy-based nonlinear viscosity for fourier approximations of conservation laws. Comptes Rendus Mathematique, 346(13-14):801–806, July 2008.


J.-L. Guermond and B. Popov. Fast estimation of the maximum wave speed in the Riemann problem for the Euler equations. Journal of Computational Physics, 321:908–926, 2016.


J.-L. Guermond and B. Popov. Invariant domains and first-order continuous finite element approximation for hyperbolic systems. SIAM Journal on Numerical Analysis, 54(4):2466–2489, 2016.


J.-L. Guermond, M. Nazarov, B. Popov, and I. Tomas. Second-order invariant domain preserving approximation of the Euler equations using convex limiting. SIAM Journal on Scientific Computing, 40(5):A3211–A3239, 2018.


R.J. Guyan. Reduction of stiffness and mass matrices. AIAA Journal, 3(2):380–380, February 1965.


R. Hartmann and P. Houston. Adaptive discontinuous Galerkin finite element methods for the compressible Euler equations. Journal of Computational Physics, 183(2):508–532, 2002.


R. Hartmann and P. Houston. Adaptive discontinuous Galerkin finite element methods for nonlinear hyperbolic conservation laws. Journal on Scientific Computing, 24(3):979–1004, 2003.


R. Hartmann. Adaptive Finite Element Methods for the Compressible Euler Equations. PhD thesis, Universität Heidelberg, 2002.


Johannes Heinz, Peter Munch, and Manfred Kaltenbacher. High-order non-conforming discontinuous Galerkin methods for the acoustic conservation equations. International Journal for Numerical Methods in Engineering, 124(9):2034–2049, 2022.


T. Heister and G. Rapin. Efficient augmented lagrangian-type preconditioning for the oseen problem using grad-div stabilization. International Journal for Numerical Methods in Fluids, 71:118–134, 2013.


T. Heister, J. Dannberg, R. Gassmöller, and W. Bangerth. High accuracy mantle convection simulation through modern numerical methods. ii: Realistic models and problems. Geophysical Journal International, 210:833–851, 2017.


L. Heltai and F. Costanzo. Variational implementation of immersed finite element methods. Computer Methods in Applied Mechanics and Engineering, 229-232:110–127, July 2012.


Félix Henri, Mathieu Coquerelle, and Pierre Lubin. Geometrical level set reinitialization using closest point method and kink detection for thin filaments, topology changes and two-phase flows. Journal of Computational Physics, 448:110704, 2022.


Marlis Hochbruck, Tomislav Pazur, Andreas Schulz, Ekkachai Thawinan, and Christian Wieners. Efficient time integration for discontinuous Galerkin approximations of linear wave equations. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 95(3):237–259, sep 2014.


Torsten Hoefler, Christian Siebert, and Andrew Lumsdaine. Scalable communication protocols for dynamic sparse data exchange. ACM Sigplan Notices, 45(5):159–168, 2010.


G.A. Holzapfel and J.C. Simo. A new viscoelastic constitutive model for continuous media at finite thermomechanical changes. International Journal of Solids and Structures, 33(20–22):3019–3034, August 1996.


G.A. Holzapfel. Nonlinear Solid Mechanics: A Continuum Approach for Engineering. John Wiley & Sons Ltd., West Sussex, England, 2007.


P. Houston and E. Süli. A note on the design of hp-adaptive finite element methods for elliptic partial differential equations. Computer Methods in Applied Mechanics and Engineering, 194(2):229–243, 2005.


V. John and P. Knobloch. On discontinuity—capturing methods for convection—diffusion equations. In Numerical Mathematics and Advanced Applications, pages 336–344. Springer, 2006.


C. Johnson and J. Pitkäranta. An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation. Mathematics of Computation, 46(173):1–26, 1986.


G. Kanschat. Parallel and Adaptive Galerkin Methods for Radiative Transfer Problems. Dissertation, Universität Heidelberg, 1996.


G. Kanschat. Notes on applied mathematics: Iterative methods, schwarz preconditioners and multigrid. 2015.


O.A. Karakashian and F. Pascal. A posteriori error estimates for a discontinuous Galerkin approximation of second-order elliptic problems. SIAM Journal on Numerical Analysis, 41(6):2374–2399, 2003.


C. T. Kelley. Newton's method in mixed precision. SIAM Review, 64:191–211, 2022.


R.B. Kellogg. On the Poisson equation with intersecting interfaces. Applicable Analysis, 4(2):101–129, 1974.


D.W. Kelly, J.P. De S. R. Gago, O.C. Zienkiewicz, and I. Babuska. A posteriori error analysis and adaptive processes in the finite element method: Part I–error analysis. International Journal for Numerical Methods in Engineering, 19:1593–1619, 1983.


C.A. Kennedy, M.H. Carpenter, and R.M. Lewis. Low-storage, explicit Runge–Kutta schemes for the compressible Navier–Stokes equations. Applied Numerical Mathematics, 35:177–219, 2000.


N. Koprowski-Theiss, M. Johlitz, and S. Diebels. Characterizing the time dependence of filled EPDM. Rubber Chemistry and Technology, 84(2):147–165, June 2011.


J. Korelc and P. Wriggers. Automation of Finite Element Methods. Springer Nature, 2016.


L.I.G. Kovasznay. Laminar flow behind a two-dimensional grid. In Mathematical Proceedings of the Cambridge Philosophical Society, volume 44, pages 58–62. Cambridge University Press, 1948.


M. Kronbichler and K. Kormann. Fast matrix-free evaluation of discontinuous Galerkin finite element operators. ACM Transactions on Mathematical Software, 45(3):29/1–40, 2019.


M. Kronbichler and K. Ljungkvist. Multigrid for matrix-free high-order finite element computations on graphics processors. ACM Transactions on Parallel Computing (TOPC), 6(1):2/1–32, 2019.


M. Kronbichler and W.A. Wall. A performance comparison of continuous and discontinuous galerkin methods with fast multigrid solvers. SIAM Journal on Scientific Computing, 40(5):A3423–A3448, 2018.


M. Kronbichler, T. Heister, and W. Bangerth. High accuracy mantle convection simulation through modern numerical methods. Geophysical Journal International, 191:12–29, 2012.


M. Kronbichler, S. Schoeder, C. Müller, and W.A. Wall. Comparison of implicit and explicit hybridizable discontinuous Galerkin methods for the acoustic wave equation. International Journal for Numerical Methods in Engineering, 106(9):712–739, 2016.


Martin Kronbichler, Ababacar Diagne, and Hanna Holmgren. A fast massively parallel two-phase flow solver for microfluidic chip simulation. The International Journal of High Performance Computing Applications, 32(2):266–287, 2018.


Damien Lebrun-Grandié, Andrey Prokopenko, Bruno Turcksin, and Stuart R Slattery. Arborx: A performance portable geometric search library. ACM Transactions on Mathematical Software (TOMS), 47(1):1–15, 2020.


H. Li and X. Zhang. Superconvergence of C \(^0\)-Q \(^k\) finite element method for elliptic equations with approximated coefficients. Journal of Scientific Computing, 82(1), December 2020.


L.-D. Liao and G.-F. Zhang. Preconditioning of complex linear systems from the helmholtz equation. Computers & Mathematics with Applications, 72:2473–2485, 2016.


C. Linder, M. Tkachuk, and C. Miehe. A micromechanically motivated diffusion-based transient network model and its incorporation into finite rubber viscoelasticity. Journal of the Mechanics and Physics of Solids, 59(10):2134–2156, October 2011.


K. Ljungkvist. Matrix-free finite-element computations on graphics processors with adaptively refined unstructured meshes. In Proceedings of the 25th High Performance Computing Symposium, HPC '17, pages 1/1–12, 2017.


A. Logg, K.-A. Mardal, and G. Wells, editors. Automated Solution of Differential Equations by the Finite Element Method. Springer Berlin Heidelberg, 2012.


R. Lohner. Edge-Based Compressible Flow Solvers. John Wiley & Sons, Ltd, 2008.


J. Lottes. Optimal polynomial smoothers for multigrid v-cycles. arXiv preprint arXiv:2202.08830, 2022.


R.E. Lynch, J.R. Rice, and D.H. Thomas. Direct solution of partial difference equations by tensor product methods. Numerische Mathematik, 6(1):185–199, dec 1964.


C. Mavriplis. Adaptive mesh strategies for the spectral element method. Computer Methods in Applied Mechanics and Engineering, 116(1):77–86, 1994.


S. McConnell. Code Complete. Microsoft Press, second edition, 2004.


J.M. Melenk and I. Babuska. The partition of unity finite element method: Basic theory and applications. Computer Methods in Applied Mechanics and Engineering, 139(1–4):289–314, 1996.


J.M. Melenk and B.I. Wohlmuth. On residual-based a posteriori error estimation in hp-FEM. Advances in Computational Mathematics, 15(1):311–331, 2001.


W.F. Mitchell and M.A. McClain. A comparison of hp-adaptive strategies for elliptic partial differential equations. ACM Transactions on Mathematical Software, 41(1):2/1–39, 2014.


W.F. Mitchell. The hp‐multigrid method applied to hp‐adaptive refinement of triangular grids. Numerical Linear Algebra with Applications, 17(2-3):211–228, April 2010.


P. Monk. Finite Element Methods for Maxwell's Equations. Numerical Mathematics and Scientific Computation. Oxford University Press, 2003.


M. Mu. PDE.Mart: A network-based problem-solving environment for PDEs. ACM Transactions on Mathematical Software, 31(4):508–531, 2005.


P. Munch, K. Kormann, and M. Kronbichler. An efficient, matrix-free finite-element library for high-dimensional partial differential equations. ACM Transactions on Mathematical Software, 47(4):33/1–34, September 2021.


P. Munch, K. Ljungkvist, and M. Kronbichler. Efficient application of hanging-node constraints for matrix-free high-order FEM computations on CPU and GPU. In Lecture Notes in Computer Science, pages 133–152. Springer International Publishing, 2022.


P. Munch, T. Heister, L. Prieto Saavedra, and M. Kronbichler. Efficient distributed matrix-free multigrid methods on locally refined meshes for FEM computations. ACM Transactions on Parallel Computing, 10(1):3/1–38, March 2023.


N.C. Nguyen and J. Peraire. Hybridizable discontinuous Galerkin methods for partial differential equations in continuum mechanics. Journal of Computational Physics, 231(18):5955–5988, 2012.


N.C. Nguyen, J. Peraire, and B. Cockburn. High-order implicit hybridizable discontinuous Galerkin methods for acoustics and elastodynamics. Journal of Computational Physics, 230(10):3695 – 3718, 2011.


J. Nocedal and S.J. Wright. Numerical Optimization. Springer Series in Operations Research. Springer, New York, 1999.


J. Nocedal and S. Wright. Numerical Optimization. Springer New York, 2006.


J. Nocedal, A. Wächter, and R.A. Waltz. Adaptive barrier update strategies for nonlinear interior methods. SIAM Journal on Optimization, 19(4):1674–1693, January 2009.


K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, and A.A. Firsov. Electric field effect in atomically thin carbon films. Science, 306:666, 2004.


Elin Olsson and Gunilla Kreiss. A conservative level set method for two phase flow. Journal of computational physics, 210(1):225–246, 2005.


Y.H. Pao. Electromagnetic forces in deformable continua. In S. Nemat-Nasser, editor, Mechanics Today, volume 4 of Pergamon Mechanics Today Series, chapter IV, pages 209–305. Elsevier, New York, 1978.


C. Park and D. Sheen. P1-nonconforming quadrilateral finite element methods for second-order elliptic problems. SIAM Journal on Numerical Analysis, 41(2):624–640, 2003.


J.-P. Pelteret and P. Steinmann. Magneto-active polymers: Fabrication, characterisation, modelling and simulation at the micro- and macro-scale. De Gruyter Mouton, 1 edition, 2019.


J.-P. Pelteret, B. Walter, and P. Steinmann. Application of metaheuristic algorithms to the identification of nonlinear magneto-viscoelastic constitutive parameters. Journal of Magnetism and Magnetic Materials, 464:116–131, 2018.


Charles S Peskin. Numerical analysis of blood flow in the heart. Journal of computational physics, 25(3):220–252, 1977.


M. Phillips and P. Fischer. Optimal chebyshev smoothers and one-sided v-cycles. arXiv preprint arXiv:2210.03179, 2022.


D.A. Di Pietro and A. Ern. Mathematical Aspects of Discontinuous Galerkin Methods. Mathématiques et Applications. Springer Berlin Heidelberg, 2011.


D.A. Di Pietro and A. Ern. Mathematical aspects of discontinuous Galerkin methods, volume 69. Springer Science & Business Media, 2011.


T. Pryer. Discontinuous Galerkin methods for the p-biharmonic equation from a discrete variational perspective. Electronic Transactions of Numerical Analysis, 41:328–349, 2014.


R. Rannacher and F.-T. Suttmeier. A feed-back approach to error control in finite element methods: Application to linear elasticity. Computational Mechanics, 19(5):434–446, 1997.


R. Rannacher and F.-T. Suttmeier. A posteriori error control in finite element methods via duality techniques: Application to perfect plasticity. Computational Mechanics, 21(2):123–133, 1998.


R. Rannacher and F.-T. Suttmeier. A posteriori error estimation and mesh adaptation for finite element models in elasto-plasticity. Computer Methods in Applied Mechanics and Engineering, 176(1):333–361, 1999.


T. Richter. Parallel Multigrid Method for Adaptive Finite Elements with Application to 3D Flow Problems. PhD thesis, Universität Heidelberg, 2005.


B. Rivière, M.F. Wheeler, and V. Girault. Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. Part I. Computational Geosciences, 3(3):337–360, 1999.


Y. Saad and M.H. Schultz. GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing, 7(3):856–869, July 1986.


Y. Saad. A Flexible Inner-Outer Preconditioned GMRES Algorithm. Technical Report 91-279, Minnesota Supercomputer Institute, University of Minnesota, 1991.


R.I. Saye. High-Order Quadrature Methods for Implicitly Defined Surfaces and Volumes in Hyperrectangles. SIAM Journal on Scientific Computing, 37(2):A993–A1019, January 2015.


N. Schlömer. quadpy: Your one-stop shop for numerical integration in Python, 2021.


S. Schoeder, K. Kormann, W.A. Wall, and M. Kronbichler. Efficient explicit time stepping of high order discontinuous Galerkin schemes for waves. SIAM Journal on Scientific Computing, 40(6):C803–C826, 2018.


M. Schwartz. Principles of Electrodynamics. International Series in Pure and Applied Physics. McGraw-Hill Book Company, New York, 1972.


Mark S. Shephard. Linear multipoint constraints applied via transformation as part of a direct stiffness assembly process. International Journal for Numerical Methods in Engineering, 20(11):2107–2112, nov 1984.


D. Silvester and A. Wathen. Fast iterative solution of stabilised Stokes systems. Part II: Using general block preconditioners. SIAM Journal on Numerical Analysis, 31:1352–1367, 1994.


B. Smith, P. Bjorstad, and W. Gropp. Domain decomposition: parallel multilevel methods for elliptic partial differential equations. Cambridge University Press, 2004.


C.E. Stanley and F.W. Homer. Choosing the forcing terms in an inexact Newton method. SIAM Journal on Scientific Computing, 17(1):16–32, 1996.


H.R. Stoll. The relationship between put and call option prices. The Journal of Finance, 24(5):801–824, 1969.


F.-T. Suttmeier. Adaptive Finite Element Approximation of Problems in Elasto-Plasticity Theory. Dissertation, Universität Heidelberg, 1996.


C. Taylor and P. Hood. A numerical solution of the Navier-Stokes equations using the finite element technique. Computers & Fluids, 1(1):73–100, 1973.


A. Toselli and O. Widlund. Domain decomposition methods-algorithms and theory, volume 34. Springer Science & Business Media, 2006.


C. Truesdell and R. Toupin. Encyclopedia of Physics: Principles of Thermodynamics and Statics, volume 1, chapter 2: The classical field theories, pages 226–794. Springer-Verlag Berlin Heidelberg, 1960.


K. Tselios and T.E. Simos. Optimized Runge–Kutta methods with minimal dispersion and dissipation for problems arising from computational acoustics. Physics Letters A, 363:38–48, 2007.


P. Tsuji, B. Engquist, and L. Ying. A sweeping preconditioner for time-harmonic Maxwell's equations. Journal of Computational Physics, 231:3770–3783, 2012.


Salih Ozen Unverdi and Grétar Tryggvason. A front-tracking method for viscous, incompressible, multi-fluid flows. Journal of computational physics, 100(1):25–37, 1992.


R. S. Varga. Matrix iterative analysis. Springer, Berlin, 2nd edition, 2009.


A. Wächter and L.T. Biegler. On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Mathematical Programming, 106(1):25–57, April 2005.


Z. Wang, G. Harper, P. O'Leary, J. Liu, and S. Tavener. deal.II implementation of a weak Galerkin finite element solver for darcy flow. In Lecture Notes in Computer Science, pages 495–509. Springer International Publishing, 2019.


G.N. Wells and N.T. Dung. A C \(^0\) discontinuous Galerkin formulation for Kirchhoff plates. Computer Methods in Applied Mechanics and Engineering, 196(35-36):3370–3380, July 2007.


F.D. Witherden and P.E. Vincent. On the identification of symmetric quadrature rules for finite element methods. Computers & Mathematics with Applications, 69(10):1232–1241, 2015.


J.-Y. Yang, S.-C. Yang, Y.-N. Chen, and C.-A. Hsu. Implicit weighted eno schemes for the three-dimensional incompressible navier–stokes equations. Journal of Computational Physics, 146:464–487, 1998.


S.T. Zalesak. Fully multidimensional flux-corrected transport algorithms for fluids. Journal of Computational Physics, 31(3):335–362, 1979.


S. Zampini. Pcbddc: a class of robust dual-primal methods in petsc. SIAM Journal on Scientific Computing, 38(5):S282–S306, 2016.


J. Zhang, J. Brown, S. Balay, J. Faibussowitsch, M. Knepley, O. Marin, R. Mills, T. Munson, B. F. Smith, and S. Zampini. The PetscSF scalable communication layer. IEEE Transactions on Parallel and Distributed Systems, 33(04):842–853, apr 2022.


F. Zhang. The Schur Complement and its Applications. Springer, 2005.