> in the whole domain, where u is finite element function on mesh_u and
> the basis function phi_i is defined on mesh_v. If the function U is
> linear, as explained in step-28, it can be calcuated by finding the
> common finest mesh {K} between mesh_u and mesh_v and then expressing u
> to be the combination of basis function defined on mesh_u. Now The
> problem seems that we can not calculate this integration in K, where K
> is active in mesh_u but not active in mesh_v. This is because we can
> not obtain the value of u on the integration points in the children of
> K. The only way seems that we had to approximate U(u) by the finite
> element function u_h defined on the mesh_u.
Yes. I'm afraid the only practical method would be to project U(u) into the
finite element space and interpolate it down to the cells of the common
mesh. Alternatively, you can of course project it into a higher order
finite element space and go through the whole derivation again to
integrate the basis functions of your finite element space against the
basis functions of a higher order space.
> I looked through the function assemble_cross_group_rhs_recursive. The
> variable prolongation_matrix should present
>
> B_cB_c^\prime… B_c^{(k)}
>
> as given this notation in the introduction of step-28.
>
> In case of
>
> cell_g->level() > cell_g_prime->level()),
>
> this means that K is active in mesh g^\prime, but not active in mesh
> g, which corresponding to the case 3. We should multiply the transpose
> of the prolongation matrix (prolongation_matrix). But in the code, the
> prolongation matrix, not its transpose is multiplied!
Hm. Yaqi, do you recall the code well enough to say whether the code is
correct or not?
> Some writting errors seems occurs in the introduction of step-28. I
> try to modify these errors.
Thanks, I've checked them in!
Best
W.
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Wolfgang Bangerth email: [email protected]
www: http://www.math.tamu.edu/~bangerth/
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