On 1/28/22 7:56 AM, [email protected] wrote:
I am looking for a way to obtain the distribution of ∇.(∇C/|∇C|) where C is
the main variable and I have its distribution (values, gradients and
laplacians) over the domain. This is used for finding the normal vector and
its divergence over the moving interface of two materials in a simulation. I
would appreciate any suggestions you might have.
When you say "obtain the distribution of ..." do you mean that you want to
evaluate that quantity at individual (quadrature) points? Or what do you want
to do with it?
The quantity you are looking at is not well defined for the usual finite
elements: grad C is a disontinuous function, and taking the divergence is
going to exacerbate the problems with this expression. The question therefore
is what you want to do with it. A common approach is to use it in a weak
formulation where you can integrate by parts to get rid of the divergence.
Best
W.
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Wolfgang Bangerth email: [email protected]
www: http://www.math.colostate.edu/~bangerth/
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