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

#include <armadillo>
#include <stdio.h>
#include <string.h>
#include <algorithm>
#include <new>
#include <ostream>
#include <string>
#include <vector>
#include "fem/update_flags.hh"
#include "system/exceptions.hh"

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Classes
class	Dof

class	FunctionSpace

class	FiniteElement< dim >
	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 , FEVector = 1 , FEVectorContravariant = 2 , FEVectorPiola = 3 , FETensor = 4 , FEMixedSystem = 5 }

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

◆ DofType

enum DofType

Enumerator
Value

Definition at line 43 of file finite_element.hh.

◆ FEType

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, FEVector, value ref_value

FETensor 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|

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

The transformation itself is done in FEValuesBase::fill_..._data() methods.

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

Enumerator
FEScalar
FEVector
FEVectorContravariant
FEVectorPiola
FETensor
FEMixedSystem

Definition at line 199 of file finite_element.hh.

Classes