Reference documentation for deal.II version 8.4.1
Numerical algorithms

## Namespaces

DerivativeApproximation

MatrixCreator

MatrixTools

VectorTools

## Classes

class  KellyErrorEstimator< dim, spacedim >

class  SolutionTransfer< dim, VectorType, DoFHandlerType >

struct  SolutionTransfer< dim, VectorType, DoFHandlerType >::Pointerstruct

## Detailed Description

This module groups a diverse set of classes that generally implement some sort of numerical algorithm on top all the basic triangulation, DoFHandler, and finite element classes in the library. They are generally unconnected to each other.

Some of the classes, like DerivativeApproximation, KellyErrorEstimator and SolutionTransfer, act on solutions already obtained, and compute derived quantities in the first two cases, or help transferring a set of vectors from one mesh to another.

The namespaces MatrixCreator, MatrixTools, and VectorTools provide an assortment of services, such as creating a Laplace matrix, projecting or interpolating a function onto the present finite element space, etc. The difference to the functions in the DoFTools and FETools functions is that they work on vectors (i.e. members of a finite element function space on a given triangulation) or help in the creation of it. On the other hand, the DoFTools functions only act on a given DoFHandler object without reference to a data vector, and the FETools objects generally work with finite element classes but again without any associated data vectors.

## Enumeration Type Documentation

template<int dim, int spacedim = dim>

The enum type given to the class functions to decide on the scaling factors of the facial integrals.

Enumerator
cell_diameter_over_24

Kelly error estimator with the factor $$\frac {h}{24}$$.

face_diameter_over_twice_max_degree

the boundary residual estimator with the factor $$\frac {h_F}{2 max(p^+,p^-)}$$.

Definition at line 260 of file error_estimator.h.

template<int dim, typename VectorType = Vector<double>, typename DoFHandlerType = DoFHandler<dim>>
 private

Declaration of PreparationState that denotes the three possible states of the SolutionTransfer: being prepared for 'pure refinement', prepared for 'coarsening and refinement' or not prepared.

Definition at line 434 of file solution_transfer.h.

Denote which norm/integral is to be computed by the integrate_difference() function of this namespace. The following possibilities are implemented:

Enumerator
mean

The function or difference of functions is integrated on each cell.

L1_norm

The absolute value of the function is integrated.

L2_norm

The square of the function is integrated and the the square root of the result is computed on each cell.

Lp_norm

The absolute value to the pth power is integrated and the pth root is computed on each cell. The exponent p is the last parameter of the function.

Linfty_norm

The maximum absolute value of the function.

H1_seminorm

L2_norm of the gradient.

Hdiv_seminorm

L2_norm of the divergence of a vector field

H1_norm

The square of this norm is the square of the L2_norm plus the square of the H1_seminorm.

W1p_seminorm

Lp_norm of the gradient.

W1p_norm

same as H1_norm for Lp.

W1infty_seminorm

Linfty_norm of the gradient.

W1infty_norm

same as H1_norm for Linfty.

Definition at line 324 of file vector_tools.h.