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LSFEM for incompressible flow

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Old   January 14, 2010, 13:14
Default LSFEM for incompressible flow
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Hi all,

I try to write a least square finite element code to solve the incompressible navier stokes equations.

The equations in u,w,p formulation are a system of 8 first order ODE, they can be writed as
A1 * du/dx + A2 * du/dy + A3 * du/dz + A * u with u={vx,vy,vz,wx,wy,wz,p} or in short L*u = F.

The least square finite element formulation give for the element matrix and the element vector

Ke = integral of { transpose (L*Nj) * (L*Ni)}
Fe = integral of { transpose (L*Nj) * F }

It look simple but It don't works when I put it in practice. That is what I do :

For each element
For i=1 to number of nodes in the element
I compute L*Nj
I compute the matrix vector product Fe = L*Nj * F
I assemble this local vector to the global vector

For j=1 to number of nodes in the element
I compute L*Ni
I compute the matrix product betxeen the transpose of L*Nj and L*Ni
I assemble this local matrix to the global matrix

Do you see my mistake ?
Maybe do you know a public source code in free access from the web using the LS-FEM strategy ?

Best regards,

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Old   January 14, 2010, 18:28
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I think I may help you about this. I do have one code to solve the incompressible N-S equations. Please contact me via Email if interested.
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