[Dune] [#870] volume() is not precise for non-affine geometries

Dune flyspray at dune-project.org
Mon Feb 14 14:33:55 CET 2011


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The following task has a new comment added:

FS#870 - volume() is not precise for non-affine geometries
User who did this - Andreas Dedner (dedner)

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Unfortunately it is quite a bit more complicated I think:
We are talking about a face of a hexahedron. That is given by a mapping F
from R=[0,1]^2 -> S subset R^3. The volume can be computed by
int_R sqrt(|det ATA|) where A=DF.
Now entries in A are linear polynomials, thus ATA has entries which are
quadratic and det ATA gives us order 4 polynomials. And then we are taking the square root of all
that...
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