Hi all,
after my naive approach yesterday, I now try to formulate my problem more
clearly. What I am interested in is the discretization of Stokes equation
(here in weak form)
a(y,v)+b(p,v)=(u,v) plus incompressibility and boundary conditions.
Note that this in my case is a constraint for an optimization problem. If I
now use Q2-Q1 elements I get
Ky+B^{T}p=M_y u
if I discretize the control u with Q2 elements. I am now interested in
discretizing the right hand side u with Q1 elements so that
I get
Ky+B^{T}p=Nu where N is a rectangular matrix stemming from the fact the the
v components are Q2 and the u components are Q1.
I now want to assemble N. The ingredients I have are the Stokes FE system
from which I have assembled K, B, M_y,M_p and am now
looking for a way to get the rectangular N.
I guess if the numbering of the nodes is such that K=blkdiag(K_1,K_2) for
two components I could assemble a matrix [M_y,N_1^{T};N_1 M_p]
and then construct my N from the N_1 block. Would this be a sensible way to
approach this?
Any suggestions are more than welcome.
Thanks all,
Martin
--
*Martin Stoll*
*Postdoctoral Research Fellow*
Computational Methods in Systems and Control Theory
Max Planck Institute for Dynamics of Complex Technical Systems
Sandtorstr. 1
D-39106 Magdeburg
Germany
Email: [email protected]
URL : http://www.mpi-magdeburg.mpg.de/people/stollm
Tel :+49 391 6110 384
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