LocalIntegrators::L2 Namespace Reference

Local integrators related to L²-inner products. More...

Functions
template<int dim>
void	mass_matrix (FullMatrix< double > &M, const FEValuesBase< dim > &fe, const double factor=1.)
template<int dim>
void	weighted_mass_matrix (FullMatrix< double > &M, const FEValuesBase< dim > &fe, const std::vector< double > &weights)
template<int dim, typename number >
void	L2 (Vector< number > &result, const FEValuesBase< dim > &fe, const std::vector< double > &input, const double factor=1.)
template<int dim, typename number >
void	L2 (Vector< number > &result, const FEValuesBase< dim > &fe, const VectorSlice< const std::vector< std::vector< double > > > &input, const double factor=1.)
template<int dim>
void	jump_matrix (FullMatrix< double > &M11, FullMatrix< double > &M12, FullMatrix< double > &M21, FullMatrix< double > &M22, const FEValuesBase< dim > &fe1, const FEValuesBase< dim > &fe2, const double factor1=1., const double factor2=1.)

Detailed Description

Local integrators related to L²-inner products.

Author

Guido Kanschat

Date

2010

Function Documentation

mass_matrix()

template<int dim>

void LocalIntegrators::L2::mass_matrix	(	FullMatrix< double > &	M,
		const FEValuesBase< dim > &	fe,
		const double	factor = 1.
	)

The mass matrix for scalar or vector values finite elements.

\[ \int_Z uv\,dx \quad \text{or} \quad \int_Z \mathbf u\cdot \mathbf v\,dx \]

Likewise, this term can be used on faces, where it computes the integrals

\[ \int_F uv\,ds \quad \text{or} \quad \int_F \mathbf u\cdot \mathbf v\,ds \]

Author

Guido Kanschat

Date

2008, 2009, 2010

Definition at line 53 of file l2.h.

weighted_mass_matrix()

template<int dim>

void LocalIntegrators::L2::weighted_mass_matrix	(	FullMatrix< double > &	M,
		const FEValuesBase< dim > &	fe,
		const std::vector< double > &	weights
	)

The weighted mass matrix for scalar or vector values finite elements.

\[ \int_Z \omega(x) uv\,dx \quad \text{or} \quad \int_Z \omega(x) \mathbf u\cdot \mathbf v\,dx \]

Likewise, this term can be used on faces, where it computes the integrals

\[ \int_F \omega(x) uv\,ds \quad \text{or} \quad \int_F \omega(x) \mathbf u\cdot \mathbf v\,ds \]

The size of the vector weights must be equal to the number of quadrature points in the finite element.

Author

Guido Kanschat

Date

2014

Definition at line 105 of file l2.h.

L2() [1/2]

template<int dim, typename number >

void LocalIntegrators::L2::L2	(	Vector< number > &	result,
		const FEValuesBase< dim > &	fe,
		const std::vector< double > &	input,
		const double	factor = 1.
	)

L²-inner product for scalar functions.

\[ \int_Z fv\,dx \quad \text{or} \quad \int_F fv\,ds \]

Author

Guido Kanschat

Date

2008, 2009, 2010

Definition at line 153 of file l2.h.

L2() [2/2]

template<int dim, typename number >

void LocalIntegrators::L2::L2	(	Vector< number > &	result,
		const FEValuesBase< dim > &	fe,
		const VectorSlice< const std::vector< std::vector< double > > > &	input,
		const double	factor = 1.
	)

L²-inner product for a slice of a vector valued right hand side.

\[ \int_Z \mathbf f\cdot \mathbf v\,dx \quad \text{or} \quad \int_F \mathbf f\cdot \mathbf v\,ds \]

Author

Guido Kanschat

Date

2008, 2009, 2010

Definition at line 178 of file l2.h.

jump_matrix()

template<int dim>

void LocalIntegrators::L2::jump_matrix	(	FullMatrix< double > &	M11,
		FullMatrix< double > &	M12,
		FullMatrix< double > &	M21,
		FullMatrix< double > &	M22,
		const FEValuesBase< dim > &	fe1,
		const FEValuesBase< dim > &	fe2,
		const double	factor1 = 1.,
		const double	factor2 = 1.
	)

The jump matrix between two cells for scalar or vector values finite elements. Note that the factor \(\gamma\) can be used to implement weighted jumps.

\[ \int_F [\gamma u][\gamma v]\,ds \quad \text{or} \int_F [\gamma \mathbf u]\cdot [\gamma \mathbf v]\,ds \]

Using appropriate weights, this term can be used to penalize violation of conformity in H¹.

Author

Guido Kanschat

Date

2008, 2009, 2010

Definition at line 209 of file l2.h.