OptFEM2D Toolbox for Matlab  V1.2b1
Matlab/Octave Optimized P1-Lagrange Finite Element Method in 2D
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validStiffP1.m File Reference

Validation function for the assembly of the stiffness matrix for $P_1$-Lagrange finite element method. More...

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Functions

function  validStiffP1 ()
 Validation function for the assembly of the stiffness matrix for $P_1$-Lagrange finite element method.
 
function  validStiffP1>checkTest1 (Test)
 
function  validStiffP1>checkTest2 (Test)
 
function  validStiffP1>checkTest3 (h, error)
 

Detailed Description

Validation function for the assembly of the stiffness matrix for $P_1$-Lagrange finite element method.

Definition in file validStiffP1.m.

Function Documentation

function validStiffP1>checkTest1 (   Test)

Definition at line 152 of file validStiffP1.m.

function validStiffP1>checkTest2 (   Test)

Definition at line 167 of file validStiffP1.m.

function validStiffP1>checkTest3 (   h,
  error 
)

Definition at line 190 of file validStiffP1.m.

function validStiffP1 ( )

Validation function for the assembly of the stiffness matrix for $P_1$-Lagrange finite element method.

The Stiffness Matrix $\Stiff$ is given by

\[\Stiff_{i,j}=\int_\DOMH \DOT{\GRAD\FoncBase_i(\q)}{\GRAD\FoncBase_j(\q)}d\q,\ \forall (i,j)\in\ENS{1}{\nq}^2\]

where $\FoncBase_i$ are $P_1$-Lagrange basis functions. This Matrix is computed by functions StiffAssemblingP1{Version} where {Version} is one of base, OptV0, OptV1 and OptV2.

  • Test 1: Computation of the Stiffness Matrix using all the versions giving errors and cputimes
  • Test 2: Computation of the integral

    \[\int_\DOM \DOT{\GRAD u(\q)}{\GRAD v(\q)}d\q \approx \DOT{\Stiff \vecb{U}}{\vecb{V}}\]

    where $\vecb{U}_i=u(\q^i)$ and $\vecb{V}_i=v(\q^i)$. Functions $u$ and $v$ are those defined in valid_FEMmatrices.
  • Test 3: One retrieves the order 2 of $P_1$-Lagrange integration

    \[|\int_\DOM \DOT{\GRAD u}{\GRAD v} -\DOT{\GRAD \Pi_h(u)}{\GRAD \Pi_h(v)}d\DOM| \leq C h^2\]

See Also
StiffAssemblingP1base, StiffAssemblingP1OptV0, StiffAssemblingP1OptV1, StiffAssemblingP1OptV2, valid_FEMmatrices, SquareMesh, GetMaxLengthEdges
Results
validStiffP1.png
figure : validStiffP1 Test 3 result
Author
François Cuvelier
Date
2012-11-26

OptFEM2DP1 [V1.2b1] - Copyright (C) 2013 CJS (LAGA)

This file is part of OptFEM2DP1. OptFEM2DP1 is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

OptFEM2DP1 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.

You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/.

Definition at line 17 of file validStiffP1.m.