PolynomialsRannacherTurek< dim > Class Template Reference

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

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	compute (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

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 41 of file polynomials_rannacher_turek.h.

Constructor & Destructor Documentation

PolynomialsRannacherTurek()

template<int dim>

PolynomialsRannacherTurek< dim >::PolynomialsRannacherTurek

(

)

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

Definition at line 24 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 33 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 199 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 66 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 103 of file polynomials_rannacher_turek.cc.

compute()

template<int dim>

void PolynomialsRannacherTurek< dim >::compute	(	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

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.

Definition at line 144 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 47 of file polynomials_rannacher_turek.h.

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

• deal.II/base/polynomials_rannacher_turek.h
• source/base/polynomials_rannacher_turek.cc