OptFEM2D  0.1
Matlab optimized FEM2D
 All Files Functions Groups Pages
Functions
validStiffP1.m File Reference

Validation function for Stiff Assembling P1 functions. More...

Go to the source code of this file.

Functions

function  validStiffP1 ()
 Validation function for Stiff Assembling P1 functions.
 
function  validStiffP1>checkTest1 (Test)
 
function  validStiffP1>checkTest2 (Test)
 
function  validStiffP1>checkTest3 (h, error)
 

Detailed Description

Validation function for Stiff Assembling P1 functions.

Definition in file validStiffP1.m.

Function Documentation

function validStiffP1>checkTest1 (   Test)

Definition at line 128 of file validStiffP1.m.

function validStiffP1>checkTest2 (   Test)

Definition at line 143 of file validStiffP1.m.

function validStiffP1>checkTest3 (   h,
  error 
)

Definition at line 166 of file validStiffP1.m.

function validStiffP1 ( )

Validation function for Stiff Assembling P1 functions.

The Stiff 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: compute Stiff Matrix using previous functions and give errors and cputimes
  • Test 2: compute

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

    where $\vecb{U}_i=u(\q^i)$ and $\vecb{V}_i=v(\q^i)$. Use fonctions $u$ and $v$ defined in valid_FEMmatrices.
  • Test 3: retrieve 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
Author
Francois Cuvelier
Date
2012-11-26

Definition at line 17 of file validStiffP1.m.