Abstract class for description of finite elements. More...
#include <armadillo>#include <stdio.h>#include <string.h>#include <algorithm>#include <boost/assign/list_of.hpp>#include <boost/exception/info.hpp>#include <new>#include <ostream>#include <string>#include <vector>#include "fem/update_flags.hh"#include "system/exceptions.hh"
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Classes | |
| class | FESystem< dim > |
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 > |
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 | 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.
* Copyright (C) 2015 Technical University of Liberec. All rights reserved.
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.
Definition in file finite_element.hh.
Enumeration Type Documentation
| enum DofType |
| Enumerator | |
|---|---|
| Value | |
Definition at line 48 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, 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 204 of file finite_element.hh.
