[Dune] [#522] Jacobian type is FieldVector< FieldVector< K,m> >
Dune
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Fri Jun 26 15:20:52 CEST 2009
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The following task has a new comment added:
FS#522 - Jacobian type is FieldVector< FieldVector< K,m> >
User who did this - Andreas Dedner (dedner)
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One reason for FV<FV> was that this is the only tensor concept
we have in Dune.
In a mixed FE framework we have g=grad.u and div g = f.
If u is vector valued then g is a matrix valued (or a tensor
of order 2). The divergence of g is not simply the trace of some matrix
but, we would need a tensor of order 3 to define the divergence.
Even for scalar u the problem is a bit more complicated since g might
be in Raviart-Thomas space (which probably has range type FV) and
grad u is FV<FV> or FM...If we had some tensor class then u would
be Tensor<0>, grad u Tensor<1> which is a vector as needed for the RT space.
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