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Reference documentation for deal.II version 9.6.0
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#include <deal.II/base/polynomials_rannacher_turek.h>
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 |
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 41 of file polynomials_rannacher_turek.h.
PolynomialsRannacherTurek< dim >::PolynomialsRannacherTurek | ( | ) |
Constructor, checking that the basis is implemented in this dimension.
Definition at line 25 of file polynomials_rannacher_turek.cc.
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overridevirtual |
Value of basis function i
at p
.
Implements ScalarPolynomialsBase< dim >.
Definition at line 35 of file polynomials_rannacher_turek.cc.
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 239 of file polynomials_rannacher_turek.h.
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inlineoverridevirtual |
Compute the first derivative of the i
th polynomial at unit point p
.
Consider using evaluate() instead.
Implements ScalarPolynomialsBase< dim >.
Definition at line 250 of file polynomials_rannacher_turek.h.
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inlineoverridevirtual |
Compute the second derivative of the i
th polynomial at unit point p
.
Consider using evaluate() instead.
Implements ScalarPolynomialsBase< dim >.
Definition at line 261 of file polynomials_rannacher_turek.h.
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inlineoverridevirtual |
Compute the third derivative of the i
th polynomial at unit point p
.
Consider using evaluate() instead.
Implements ScalarPolynomialsBase< dim >.
Definition at line 272 of file polynomials_rannacher_turek.h.
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inlineoverridevirtual |
Compute the fourth derivative of the i
th polynomial at unit point p
.
Consider using evaluate() instead.
Implements ScalarPolynomialsBase< dim >.
Definition at line 283 of file polynomials_rannacher_turek.h.
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overridevirtual |
Gradient of basis function i
at p
.
Implements ScalarPolynomialsBase< dim >.
Definition at line 68 of file polynomials_rannacher_turek.cc.
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overridevirtual |
Gradient of gradient of basis function i
at p
.
Implements ScalarPolynomialsBase< dim >.
Definition at line 113 of file polynomials_rannacher_turek.cc.
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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 162 of file polynomials_rannacher_turek.cc.
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inlineoverridevirtual |
Return the name of the space, which is RannacherTurek
.
Implements ScalarPolynomialsBase< dim >.
Definition at line 294 of file polynomials_rannacher_turek.h.
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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 211 of file polynomials_rannacher_turek.cc.
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inlineinherited |
Return the number of polynomials.
Definition at line 239 of file scalar_polynomials_base.h.
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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 248 of file scalar_polynomials_base.h.
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virtualinherited |
Return an estimate (in bytes) for the memory consumption of this object.
Reimplemented in BarycentricPolynomials< dim >, BarycentricPolynomials< 1 >, BarycentricPolynomials< 2 >, TensorProductPolynomials< dim, PolynomialType >, and TensorProductPolynomials< dim - 1 >.
Definition at line 38 of file scalar_polynomials_base.cc.
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staticconstexpr |
Dimension we are working in.
Definition at line 47 of file polynomials_rannacher_turek.h.
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privateinherited |
The highest polynomial degree of this functions represented by this object.
Definition at line 227 of file scalar_polynomials_base.h.
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privateinherited |
The number of polynomials represented by this object.
Definition at line 232 of file scalar_polynomials_base.h.