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

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.

Definition at line 40 of file polynomials_rannacher_turek.h.

Inheritance diagram for PolynomialsRannacherTurek< dim >:

[legend]

Public Member Functions
	PolynomialsRannacherTurek ()

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

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

virtual Tensor< 1, dim >	compute_1st_derivative (const unsigned int i, const Point< dim > &p) const override

virtual Tensor< 2, dim >	compute_2nd_derivative (const unsigned int i, const Point< dim > &p) const override

virtual Tensor< 3, dim >	compute_3rd_derivative (const unsigned int i, const Point< dim > &p) const override

virtual Tensor< 4, dim >	compute_4th_derivative (const unsigned int i, const Point< dim > &p) const override

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

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

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

unsigned int	n () const

virtual unsigned int	degree () const

virtual std::size_t	memory_consumption () const

Static Public Attributes
static constexpr unsigned int	dimension = dim

Private Attributes
const unsigned int	polynomial_degree

const unsigned int	n_pols

Constructor & Destructor Documentation

◆ PolynomialsRannacherTurek()

template<int dim>

PolynomialsRannacherTurek< dim >::PolynomialsRannacherTurek ( )

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

Definition at line 23 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

overridevirtual

Value of basis function i at p.

Implements ScalarPolynomialsBase< dim >.

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 evaluate() instead.

Definition at line 236 of file polynomials_rannacher_turek.h.

◆ compute_1st_derivative()

template<int dim>

Tensor< 1, dim > PolynomialsRannacherTurek< dim >::compute_1st_derivative	(	const unsigned int	i,
		const Point< dim > &	p
	)		const

inlineoverridevirtual

Compute the first derivative of the ith polynomial at unit point p.

Consider using evaluate() instead.

Implements ScalarPolynomialsBase< dim >.

Definition at line 247 of file polynomials_rannacher_turek.h.

◆ compute_2nd_derivative()

template<int dim>

Tensor< 2, dim > PolynomialsRannacherTurek< dim >::compute_2nd_derivative	(	const unsigned int	i,
		const Point< dim > &	p
	)		const

inlineoverridevirtual

Compute the second derivative of the ith polynomial at unit point p.

Consider using evaluate() instead.

Implements ScalarPolynomialsBase< dim >.

Definition at line 258 of file polynomials_rannacher_turek.h.

◆ compute_3rd_derivative()

template<int dim>

Tensor< 3, dim > PolynomialsRannacherTurek< dim >::compute_3rd_derivative	(	const unsigned int	i,
		const Point< dim > &	p
	)		const

inlineoverridevirtual

Compute the third derivative of the ith polynomial at unit point p.

Consider using evaluate() instead.

Implements ScalarPolynomialsBase< dim >.

Definition at line 269 of file polynomials_rannacher_turek.h.

◆ compute_4th_derivative()

template<int dim>

Tensor< 4, dim > PolynomialsRannacherTurek< dim >::compute_4th_derivative	(	const unsigned int	i,
		const Point< dim > &	p
	)		const

inlineoverridevirtual

Compute the fourth derivative of the ith polynomial at unit point p.

Consider using evaluate() instead.

Implements ScalarPolynomialsBase< dim >.

Definition at line 280 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

overridevirtual

Gradient of basis function i at p.

Implements ScalarPolynomialsBase< dim >.

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

overridevirtual

Gradient of gradient of basis function i at p.

Implements ScalarPolynomialsBase< dim >.

Definition at line 111 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 160 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 291 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 209 of file polynomials_rannacher_turek.cc.

◆ n()

template<int dim>

unsigned int ScalarPolynomialsBase< dim >::n ( ) const

inlineinherited

Return the number of polynomials.

Definition at line 254 of file scalar_polynomials_base.h.

◆ degree()

template<int dim>

unsigned int ScalarPolynomialsBase< dim >::degree ( ) const

inlinevirtualinherited

Return the highest polynomial degree of polynomials represented by this class. A derived class may override this if its value is different from my_degree.

Reimplemented in PolynomialsP< dim >.

Definition at line 263 of file scalar_polynomials_base.h.

◆ memory_consumption()

template<int dim>

std::size_t ScalarPolynomialsBase< dim >::memory_consumption ( ) const

virtualinherited

Return an estimate (in bytes) for the memory consumption of this object.

Reimplemented in BarycentricPolynomials< dim >, TensorProductPolynomials< dim, PolynomialType >, and TensorProductPolynomials< dim - 1 >.

Definition at line 36 of file scalar_polynomials_base.cc.

Member Data Documentation

◆ dimension

template<int dim>

constexpr unsigned int PolynomialsRannacherTurek< dim >::dimension = dim

staticconstexpr

Dimension we are working in.

Definition at line 46 of file polynomials_rannacher_turek.h.

◆ polynomial_degree

template<int dim>

const unsigned int ScalarPolynomialsBase< dim >::polynomial_degree

privateinherited

The highest polynomial degree of this functions represented by this object.

Definition at line 225 of file scalar_polynomials_base.h.

◆ n_pols

template<int dim>

const unsigned int ScalarPolynomialsBase< dim >::n_pols

privateinherited

The number of polynomials represented by this object.

Definition at line 230 of file scalar_polynomials_base.h.

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

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

Detailed Description

Public Member Functions

Static Public Attributes

Private Attributes

Constructor & Destructor Documentation

◆ PolynomialsRannacherTurek()

Member Function Documentation

◆ compute_value()

◆ compute_derivative()

◆ compute_1st_derivative()

◆ compute_2nd_derivative()

◆ compute_3rd_derivative()

◆ compute_4th_derivative()

◆ compute_grad()

◆ compute_grad_grad()

◆ evaluate()

◆ name()

◆ clone()

◆ n()

◆ degree()

◆ memory_consumption()

Member Data Documentation

◆ dimension

◆ polynomial_degree

◆ n_pols