> > ...which you compute via quadrature? Or do you compute a vector F that > corresponds to f(u) somehow? > > If you go the route via vectors you have to pay attention to *what kind > of vector you have*, namely one that does or does not incorporate > constraints. Dealing with dual space vectors (e.g., rhs vectors) is > tricky because they obey different rules than primal space vectors > (e.g., solution vectors). > I'm assembling a vector F that represent f(u); the action of f(u) on a vector field v with FE expansion coefficients V can be represented as F*V. Of course if you want to compute the L2 inner product of say, u and v, that would be U^*MV where M is the mass matrix. I actually made a wrapper class with an extra template parameter to keep track of whether a field is in H^1 or in (H^1)^* in order to keep myself from making this mistake. Do you think there might be some additional subtlety regarding either boundary of hanging node constraints in this case?
> So u_a, v_a are the same as u, v in the pointwise sense, just > interpolated from a uniform mesh to an adaptively refined one obtained > from the uniform one? > Not quite, I defined a dealii::TensorFunction object representing the exact solution and a perturbation of it that matches it along the boundary; u, v are interpolated from the TensorFunction object to the uniform mesh, u_a and v_a are interpolated from it to the non-uniform mesh. > Are you using the L2 projection? For example, for the Laplace equation, > I think you can only guarantee that the H1 seminorm error is smaller for > a finer mesh, but not necessarily the L2 error. It all depends on your > equation. > > I did not know that! I shouldn't have said projection, really I interpolated an analytic formula for the solution. > And how do the two meshes differ? > The domain is a rectangle; the grid spacing is half as large in the right half of the mesh. -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to dealii+unsubscr...@googlegroups.com. For more options, visit https://groups.google.com/d/optout.
