Reference documentation for deal.II version 8.1.0
Functions
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, 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

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 57 of file l2.h.

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 89 of file l2.h.

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 118 of file l2.h.

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 154 of file l2.h.