Reference documentation for deal.II version Git 35565f205e 2019-09-24 08:33:37 +0200
\(\newcommand{\dealcoloneq}{\mathrel{\vcenter{:}}=}\)
Public Member Functions | Static Public Attributes | List of all members
PolynomialsRannacherTurek< dim > Class Template Reference

#include <deal.II/base/polynomials_rannacher_turek.h>

Inheritance diagram for PolynomialsRannacherTurek< dim >:
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Public Member Functions

 PolynomialsRannacherTurek ()
 
double compute_value (const unsigned int i, const Point< dim > &p) const
 
template<int order>
Tensor< order, dim > compute_derivative (const unsigned int i, const Point< dim > &p) const
 
Tensor< 1, dim > compute_grad (const unsigned int i, const Point< dim > &p) const
 
Tensor< 2, dim > compute_grad_grad (const unsigned int i, const Point< dim > &p) const
 
void evaluate (const Point< dim > &unit_point, std::vector< double > &values, std::vector< Tensor< 1, dim >> &grads, std::vector< Tensor< 2, dim >> &grad_grads, std::vector< Tensor< 3, dim >> &third_derivatives, std::vector< Tensor< 4, dim >> &fourth_derivatives) const override
 
std::string name () const override
 
virtual std::unique_ptr< ScalarPolynomialsBase< dim > > clone () const override
 
- Public Member Functions inherited from ScalarPolynomialsBase< dim >
 ScalarPolynomialsBase (const unsigned int deg, const unsigned int n_polynomials)
 
 ScalarPolynomialsBase (ScalarPolynomialsBase< dim > &&)=default
 
 ScalarPolynomialsBase (const ScalarPolynomialsBase< dim > &)=default
 
virtual ~ScalarPolynomialsBase ()=default
 
unsigned int n () const
 
unsigned int degree () const
 

Static Public Attributes

static const unsigned int dimension = dim
 

Detailed Description

template<int dim>
class PolynomialsRannacherTurek< dim >

Basis for polynomial space on the unit square used for lowest order Rannacher Turek element.

The i-th basis function is the dual basis element corresponding to the dof which evaluates the function's mean value across the i-th face. The numbering can be found in GeometryInfo.

Author
Patrick Esser
Date
2015

Definition at line 42 of file polynomials_rannacher_turek.h.

Constructor & Destructor Documentation

◆ PolynomialsRannacherTurek()

Constructor, checking that the basis is implemented in this dimension.

Definition at line 25 of file polynomials_rannacher_turek.cc.

Member Function Documentation

◆ compute_value()

template<int dim>
double PolynomialsRannacherTurek< dim >::compute_value ( const unsigned int  i,
const Point< dim > &  p 
) const

Value of basis function i at p.

Definition at line 35 of file polynomials_rannacher_turek.cc.

◆ compute_derivative()

template<int dim>
template<int order>
Tensor< order, dim > PolynomialsRannacherTurek< dim >::compute_derivative ( const unsigned int  i,
const Point< dim > &  p 
) const

order-th of basis function i at p.

Consider using compute() instead.

Definition at line 212 of file polynomials_rannacher_turek.h.

◆ compute_grad()

template<int dim>
Tensor< 1, dim > PolynomialsRannacherTurek< dim >::compute_grad ( const unsigned int  i,
const Point< dim > &  p 
) const

Gradient of basis function i at p.

Definition at line 68 of file polynomials_rannacher_turek.cc.

◆ compute_grad_grad()

template<int dim>
Tensor< 2, dim > PolynomialsRannacherTurek< dim >::compute_grad_grad ( const unsigned int  i,
const Point< dim > &  p 
) const

Gradient of gradient of basis function i at p.

Definition at line 105 of file polynomials_rannacher_turek.cc.

◆ evaluate()

template<int dim>
void PolynomialsRannacherTurek< dim >::evaluate ( const Point< dim > &  unit_point,
std::vector< double > &  values,
std::vector< Tensor< 1, dim >> &  grads,
std::vector< Tensor< 2, dim >> &  grad_grads,
std::vector< Tensor< 3, dim >> &  third_derivatives,
std::vector< Tensor< 4, dim >> &  fourth_derivatives 
) const
overridevirtual

Compute values and derivatives of all basis functions at unit_point.

Size of the vectors must be either equal to the number of polynomials or zero. A size of zero means that we are not computing the vector entries.

Implements ScalarPolynomialsBase< dim >.

Definition at line 146 of file polynomials_rannacher_turek.cc.

◆ name()

template<int dim>
std::string PolynomialsRannacherTurek< dim >::name ( ) const
inlineoverridevirtual

Return the name of the space, which is RannacherTurek.

Implements ScalarPolynomialsBase< dim >.

Definition at line 223 of file polynomials_rannacher_turek.h.

◆ clone()

template<int dim>
std::unique_ptr< ScalarPolynomialsBase< dim > > PolynomialsRannacherTurek< dim >::clone ( ) const
overridevirtual

A sort of virtual copy constructor, this function returns a copy of the polynomial space object. Derived classes need to override the function here in this base class and return an object of the same type as the derived class.

Some places in the library, for example the constructors of FE_Poly, need to make copies of polynomial spaces without knowing their exact type. They do so through this function.

Implements ScalarPolynomialsBase< dim >.

Definition at line 195 of file polynomials_rannacher_turek.cc.

Member Data Documentation

◆ dimension

template<int dim>
const unsigned int PolynomialsRannacherTurek< dim >::dimension = dim
static

Dimension we are working in.

Definition at line 48 of file polynomials_rannacher_turek.h.


The documentation for this class was generated from the following files: