assemble matrix in stokes problem, projection vrs assemble

On 12 June 2012 22:01, Daniel Bare <email address hidden>wrote:

> New question #200237 on DOLFIN:
> https://answers.launchpad.net/dolfin/+question/200237
>
>
> I am implementing the Uzawa algorithm for a Stokes Problem therefore I
> need 3 matrices A, BT, B:
>
> # Define function spaces
> V = VectorFunctionSpace(mesh, "CG", 2)
> Q = FunctionSpace(mesh, "CG", 1)
>
> u = TrialFunction(V)
> v = TestFunction(V)
> p = TrialFunction(Q)
> q = TestFunction(Q)
>
> A=assemble(inner(grad(u), grad(v))*dx)
> BT=assemble(inner(v,grad(p))*dx)
> B=assemble(-q*(div(u))*dx)
>
> A, BT work well, but B should be BT transposed, and it isnt. B is wrong.

Whether B is BT transposed or not depends on the boundary conditions.

Notice that matrices in Dolfin have transposed vector product, so you can
use this method (transpmult)

Notice also that e.g. the stokes-iterative demo (or corresponding demos in
cbc.block) will give you better algorithms
than Uzawa.

Kent

> But when B is assembled implicitely in each iteration step with a given
> velocity u_current as project(-div(u_current ),Q) everything is fine.
>
> The same thing with assemble doesn't work either
> assemble(-q*(div(u_current))*dx) . But this assemble is a projection to Q
> with the scalar product (q,-div(u_current)=assemble(-q*(div(u_current))*dx)
> ? What is wrong with assemble? Why does project() work?
>
> thanks,
>
> Daniel
>
>
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