Dear all!
I've got an interesting question. I would like to implement
biharmonic Laplace equation with the strong formulation:
\Delta^2 u = f in \Omega
u = \partial_n u = 0 on \Gamma
One possibility to treat the problem is a mixed formulation.
Its variational formulation reads
Find u\in H^1_0 and w \in H^1 such that
(w,phi) + (\nabla u , \nabla phi) = 0 for phi \in H^1
(\nabla w, \nabla \psi) = (f,\psi) for \psi \in H^1_0
where (*,*) denotes the usual scalar product on the domain \Omega.
Now my question on implementation of the boundary data (maybe it is very
easy). There are two possibilities to apply boundary data:
i) MatrixTools::apply_boundary_values(...) or
ii) via constraints with constraints.distribute_local_to_global(...)
I would like to use the second one. Now, ansatz- and test functions in the
scalar products given in the problem above come from different spaces H^1
and H^1_0. How can I apply boundary data in an appropriate way?
For me, the situation is clear when dealing with normal Laplace equation:
(\nabla u,\nabla phi) = (f,phi) for all phi\in H^1_0
then I use the deal.II-function:
VectorTools::interpolate_boundary_values (...)
to apply Dirichlet values because here ansatz- and test-functions come
from the same space.
How is procedure with such a mixed formulation and different test spaces?
Thanks in advance and kind regards,
Thomas
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Thomas Wick
Universität Heidelberg
AG Numerik, Raum 213
Im Neuenheimer Feld 293
69120 Heidelberg
Tel.: +49-(0)6221 / 54-5449
E-Mail: [email protected]
Web: numerik.iwr.uni-heidelberg.de/
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