Reference documentation for deal.II version 9.1.1
\(\newcommand{\dealcoloneq}{\mathrel{\vcenter{:}}=}\)
Public Member Functions | Static Public Attributes | List of all members
PolynomialsRannacherTurek< dim > Class Template Reference

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

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()

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.


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