# Re: [deal.II] Geometric Conservation Law


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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