OptFEM2DP1 Toolbox  V1.2b3
Matlab/Octave Optimized P1-Lagrange Finite Element Method in 2D
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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 137 of file validMassP1.m.

function validMassP1>checkTest2 (   Test)

Definition at line 152 of file validMassP1.m.

function validMassP1>checkTest3 (   h,
  error 
)

Definition at line 175 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 computation times
  • 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
Copyright
See License issues

Definition at line 17 of file validMassP1.m.