Kysusik,
I'm studying step-20 tutorial example. But, I can't understand it, because it
seems to have different things compared to step-3 in terms of boundary
condition.
In the introduction of step-3, it is said that
∫Ω∇φ⋅∇u−∫∂Ωφn⋅∇u=∫Ωφf.
The test function φ has to satisfy the same kind of boundary conditions (in
mathematical terms: it needs to come from the tangent space of the set in
which we seek the solution), so on the boundary φ=0 and consequently the weak
form we are looking for reads
Since φ=0, there is no kind of boundary term(that is second term in the left
hand side of above Eq) in weak form that is (∇φ,∇u)=(φ,f),
To do this, "VectorTools::interpolate_boundary_values" and
"MatrixTools::apply_boundary_values" are used in step-3.
However, in step-20, the boundary condition is not zero anymore. Instead of
using "VectorTools::interpolate_boundary_values" and
"MatrixTools::apply_boundary_values", the boundary term for pressure is added
in the weak form. So, in assemble_system, there is part for boundary of
preesure.
As in step-20, I thought adding boundary term in weak form(in assemble_system)
can replace using the above two things. However, in step-3, Boundary is zero
unlike step-20. So there is nothing to add in assemble_system.
So, I thought it would be OK If I erase the above two things for
ZeroBoundaryCondition. But the result is not...
The error is "SolverControl::NoConvergence (it, res)".
I don't know what is the difference between erasing the two things in step-3
and inputting zero values in PressureBoundaryValues<dim>::value in step-20.
The difference that in step-3, you are imposing *strong* boundary conditions,
whereas in step-20, you are imposing *weak* boundary conditions. I suspect
that you will want to watch lectures 21.5/21.55:
http://www.math.colostate.edu/~bangerth/videos.html
And, what I have to do to apply zero boundary condition when FESystem<dim> is
used as in step-20.
Since the boundary conditions in step-20 are weak, you can just omit the term
in the assembly.
Best
W.
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Wolfgang Bangerth email: [email protected]
www: http://www.math.colostate.edu/~bangerth/
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