 Reference documentation for deal.II version Git 180dc024a7 2020-01-22 00:40:46 -0500

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

## Public Member Functions

void compute (const Point< 2 > &unit_point, std::vector< double > &values, std::vector< Tensor< 1, 2 >> &grads, std::vector< Tensor< 2, 2 >> &grad_grads) const

double compute_value (const unsigned int i, const Point< 2 > &p) const

Tensor< 1, 2 > compute_grad (const unsigned int i, const Point< 2 > &p) const

Tensor< 2, 2 > compute_grad_grad (const unsigned int i, const Point< 2 > &p) const

## Private Attributes

Table< 2, double > coef

Table< 2, double > dx

Table< 2, double > dy

Table< 2, double > dxx

Table< 2, double > dyy

Table< 2, double > dxy

## Detailed Description

The cubic polynomial space for the Adini element

This space consists of the cubic space P3 augmented by the functions xy3 and x3y.

The basis of the space is chosen to match the node functionals of the Adini element.

Todo:
This polynomial space is implemented in 2D only.

Definition at line 42 of file polynomials_adini.h.

## Constructor & Destructor Documentation

Constructor for the polynomials of the described space

Definition at line 38 of file polynomials_adini.cc.

## ◆ compute()

 void PolynomialsAdini::compute ( const Point< 2 > & unit_point, std::vector< double > & values, std::vector< Tensor< 1, 2 >> & grads, std::vector< Tensor< 2, 2 >> & grad_grads ) const

Compute the value and the first and second derivatives of each polynomial at unit_point.

The size of the vectors must either be equal 0 or equal n(). In the first case, the function will not compute these values, i.e. you indicate what you want to have computed by resizing those vectors which you want filled.

If you need values or derivatives of all polynomials then use this function, rather than using any of the compute_value(), compute_grad() or compute_grad_grad() functions, see below, in a loop over all polynomials.

Definition at line 129 of file polynomials_adini.cc.

## ◆ compute_value()

 double PolynomialsAdini::compute_value ( const unsigned int i, const Point< 2 > & p ) const

Compute the value of the ith polynomial at unit_point.

Definition at line 161 of file polynomials_adini.cc.

 Tensor< 1, 2 > PolynomialsAdini::compute_grad ( const unsigned int i, const Point< 2 > & p ) const

Compute the gradient of the ith polynomial at unit_point.

Definition at line 173 of file polynomials_adini.cc.

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

Compute the second derivative (grad_grad) of the ith polynomial at unit_point.

Definition at line 193 of file polynomials_adini.cc.

## ◆ coef

private

Store the coefficients of the polynomials in the order $$1,x,y,x^2,y^2,xy,x^3,y^3,xy^2,x^2y,x^3y,xy^3$$

Definition at line 104 of file polynomials_adini.h.

## ◆ dx

private

Store the coefficients of the x-derivative of the polynomials in the order $$1,x,y,x^2,y^2,xy,x^3,y^3,xy^2,x^2y,x^3y,xy^3$$

Definition at line 111 of file polynomials_adini.h.

## ◆ dy

private

Store the coefficients of the y-derivative of the polynomials in the order $$1,x,y,x^2,y^2,xy,x^3,y^3,xy^2,x^2y,x^3y,xy^3$$

Definition at line 117 of file polynomials_adini.h.

## ◆ dxx

private

Store the coefficients of the second x-derivative of the polynomials in the order $$1,x,y,x^2,y^2,xy,x^3,y^3,xy^2,x^2y,x^3y,xy^3$$

Definition at line 122 of file polynomials_adini.h.

## ◆ dyy

private

Store the coefficients of the second y-derivative of the polynomials in the order $$1,x,y,x^2,y^2,xy,x^3,y^3,xy^2,x^2y,x^3y,xy^3$$

Definition at line 127 of file polynomials_adini.h.

## ◆ dxy

Store the coefficients of the second mixed derivative of the polynomials in the order $$1,x,y,x^2,y^2,xy,x^3,y^3,xy^2,x^2y,x^3y,xy^3$$