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

Inheritance diagram for PolynomialsRannacherTurek< dim >:

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

virtual std::size_t	memory_consumption () 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 44 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 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 evaluate() instead.

Definition at line 214 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

inlineoverridevirtual

Return the name of the space, which is RannacherTurek.

Implements ScalarPolynomialsBase< dim >.

Definition at line 225 of file polynomials_rannacher_turek.h.

◆ clone()

template<int dim>

std::unique_ptr< ScalarPolynomialsBase< dim > > PolynomialsRannacherTurek< dim >::clone

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.