Alexander,
I am wondering if anybody has also found that the inverse of the Jacobian from
FE Values, with MappingQGeneric does not satisfy the Geometric Conservation
Law (GCL), in the sense of:
Kopriva, David A. "Metric identities and the discontinuous spectral element
method on curvilinear meshes." /Journal of Scientific Computing/ 26.3 (2006): 301.
on curvilinear elements/manifolds in 3D.
That is:
\frac{\partial }{\partial \hat{x}_1} *det(J)* \frac{\partial \hat{x}_1
}{\partial x_1} + \frac{\partial }{\partial \hat{x}_2} *det(J)* \frac{\partial
\hat{x}_2}{\partial x} + \frac{\partial }{\partial \hat{x}_3} *
det(J)*\frac{\partial \hat{x}_3 }{\partial x_1} != 0 (GCL says it should =0,
similarly for x_2 and x_3)
If so or if not, also, has anybody found a remedy to have the inverse of the
Jacobian from FE Values with MappingQGeneric to satisfy the GCL.
I'm not sure any of us have ever thought about it. (I haven't -- but I really
shouldn't speak for anyone else.) Can you explain what this equality
represents? Why should it hold?
I'm also unsure whether we've ever checked whether it holds (exactly or
approximately). Can you create a small test program that illustrates the
behavior you are seeing?
Best
W.
--
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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