OptFEM2D Toolbox for Matlab  V1.2b1
Matlab/Octave Optimized P1-Lagrange Finite Element Method in 2D
 All Files Functions Pages
Functions
validMassP1.m File Reference

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

Go to the source code of this file.

Functions

function  validMassP1 ()
 Validation function for the assembly of the mass matrix for $P_1$-Lagrange finite element method.
 
function  validMassP1>checkTest1 (Test)
 
function  validMassP1>checkTest2 (Test)
 
function  validMassP1>checkTest3 (h, error)
 

Detailed Description

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

Definition in file validMassP1.m.

Function Documentation

function validMassP1>checkTest1 (   Test)

Definition at line 151 of file validMassP1.m.

function validMassP1>checkTest2 (   Test)

Definition at line 166 of file validMassP1.m.

function validMassP1>checkTest3 (   h,
  error 
)

Definition at line 189 of file validMassP1.m.

function validMassP1 ( )

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

The Mass Matrix $\Masse$ is given by

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

where $\FoncBase_i$ are $P_1$-Lagrange basis functions. This Matrix is computed by functions MassAssemblingP1{Version} where {Version} is one of base, OptV0, OptV1 and OptV2.

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

    \[\int_\DOM u(x,y) v(x,y) dxdy \approx \DOT{\Masse \vecb{U}}{\vecb{V}}\]

    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: Ones retrieves the order 2 of $P_1$-Lagrange integration

    \[|\int_\DOM u\,v -\Pi_h(u)\,\Pi_h(v)d\DOM| \leq C h^2\]

See Also
MassAssemblingP1base, MassAssemblingP1OptV0, MassAssemblingP1OptV1, MassAssemblingP1OptV2, valid_FEMmatrices, SquareMesh, GetMaxLengthEdges
Results
validMassP1.png
figure : validMassP1 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 validMassP1.m.