Abstract class for description of finite elements. More...

#include <armadillo>
#include <map>
#include <vector>
#include <boost/assign/list_of.hpp>
#include "fem/update_flags.hh"

This graph shows which files directly or indirectly include this file:

Go to the source code of this file.

Classes
class	FESystem< dim, spacedim >
	Compound finite element on `dim` dimensional simplex. More...

class	FESideValues< dim, spacedim >
	Calculates finite element data on a side. More...

class	FEValues< dim, spacedim >
	Calculates finite element data on the actual cell. More...

class	FEValuesBase< dim, spacedim >
	Base class for FEValues and FESideValues. More...

class	FEValuesData< dim, spacedim >
	Class FEValuesData holds the arrays of data computed by Mapping and FiniteElement. More...

class	FE_P_disc< dim, spacedim >
	Discontinuous Lagrangean finite element on `dim` dimensional simplex. More...

class	Quadrature< dim >
	Base class for quadrature rules on simplices in arbitrary dimensions. More...

class	Dof

class	FunctionSpace

class	FEInternalData
	Structure for storing the precomputed finite element data. More...

class	FiniteElement< dim, spacedim >
	Abstract class for the description of a general finite element on a reference simplex in `dim` dimensions. More...

Enumerations
enum	DofType { Value = 1 }

enum	FEType { FEScalar = 0, FEVectorContravariant = 1, FEVectorPiola = 2, FETensor = 3, FEMixedSystem = 4 }

Detailed Description

Abstract class for description of finite elements.

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License version 3 as published by the Free Software Foundation. (http://www.gnu.org/licenses/gpl-3.0.en.html)

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

Author: Jan Stebel

Definition in file finite_element.hh.

Enumeration Type Documentation

enum DofType

Enumerator
Value

Definition at line 43 of file finite_element.hh.

enum FEType

Types of FiniteElement: scalar, vector-valued, tensor-valued or mixed system.

The type also indicates how the shape functions and their gradients are transformed from reference element to arbitrary element. In particular:

TYPE              OBJECT  EXPRESSION

FEScalar value ref_value

grad J^{-T} * ref_grad

FEVectorContravariant value J * ref_value

grad J^{-T} * ref_grad * J^T

FEVectorPiola value J * ref_value / |J|

grad J^{-T} * ref_grad * J^T / |J|

FETensor value not implemented

grad not implemented

FEMixedSystem value depends on sub-elements grad depends on sub-elements

Note that we use columnwise gradients, i.e. gradient of each component is a column vector.

Enumerator
FEScalar
FEVectorContravariant
FEVectorPiola
FETensor
FEMixedSystem

Definition at line 200 of file finite_element.hh.