Hello,
for solving the (ideal) MHD equations, I would like to implement two custom
shapesets:
- one for the flow part, completely discontinuous, scalar FE space,
analogy to FE_DGQ, but based on Taylor expansion in the cell center
- 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
- 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
- this I assume will be more difficult, but here I am only after
linear functions
Reasoning behind usage of these is in
https://github.com/l-korous/mhdeal/blob/master/papers/Compumag2017_MHD.pdf,
section IV.A (divergence free space), IV.B (Vertex-based limiting which
needs the Taylor-basis FE space). Currently the code in
https://github.com/l-korous/mhdeal/blob/master/code/ is failing for DG
order > 0 because of undershoots and overshoots present in the unlimited
flow solution, mag field works, but there is no divergence cleaning
employed.
Could you please point me in the right direction where to start with this
and what all needs to be done for these two new shapesets / spaces to be
employed?
Many thanks
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