Lukas,
for solving the (ideal) MHD equations, I would like to implement two custom
shapesets:
By "shapeset" do you mean "set of shape functions"?
* one for the flow part, completely discontinuous, scalar FE space, analogy
to FE_DGQ, but based on Taylor expansion in the cell center
o this should be the easy part, but I would like to ask how to go about
it in deal.ii - I would like to implement at least linear and
quadratic functions
Do you do the Taylor expansion in real space, or on the reference cell and
then map to real space?
If the former, I think you will want to look at the implementation of the
FE_DGP and FE_DGP_Monomial classes, of which at least one does something
similar IIRC.
* one for the magnetic field, a vector Hdiv space, analogy to
FE_RaviartThomas, but in this case a space of divergence-free functions
that satisfy div F = 0 within the reference cell
o this I assume will be more difficult, but here I am only after linear
functions
Again: on the reference cell or in real space?
If you work in real space, then in 2d there are 2x3 basis functions for the
linear space (two vector components, each of which has the form a+bx+cy), of
which you can eliminate one because of the divergence constraint, if I count
correctly.
If you map from the reference cell, but require that div u = 0 pointwise in
real space, then things may be more complicated.
Best
Wolfgang
--
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Wolfgang Bangerth email: [email protected]
www: http://www.math.colostate.edu/~bangerth/
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