Hello Daniel, I made a big mistake. I was somehow under the impression that Fipy is a finite element library. No wonder that I couldn't find information on the base functions of the elements that are used. Sorry for the confusion. getfem++ seems to solve my problem.
Thanks alot! Benjamin Am 17.01.2014 00:26, schrieb Daniel Wheeler: > On Wed, Jan 15, 2014 at 5:15 PM, Benjamin Hepp > <[email protected]> wrote: >> Hello, >> >> my question from a few days ago might have been a bit imprecise. I >> reformulate it and hope this helps: >> >> I could not find any details in the FiPy documentation so I assume it is >> using first order Lagrange elements psi_i, where i is the element index. > > I guess that is correct. FiPy just uses linear interpolation between > cell centers. > >> I would like to compute the integrals >> <psi_i, psi_j> >> and >> <grad psi_i, grad psi_j> >> for each i, j. Is this possible with FiPy? > > This is confusing. In the FVM, $\psi_i$ only really means anything in > cell $i$. By definition, > > \psi_i = \int \psi dV_i / \int dV_i > > over a given cell. The integrals might not make sense in the context > of the FVM, while making sense in terms of the FEM. This may be to do > with the notion of local support in FEM, where the $phi_i$ is defined > on the whole domain, but is only non-zero in the neighbourhood of > element $i$ so the integral makes sense. If one was to do this naively > with the output from fipy, then you would just have a diagonal matrix, > which doesn't show you anything. What you need is a reconstruction of > the non-averaged discretized $\psi$'s. I don't believe that FiPy has > any inbuilt functionality to do this. > > Hope that helps or at least clarifies things a bit. >
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