[CIG-CS] Discontinuous viscosity

Wolfgang Bangerth bangerth at math.tamu.edu
Sun Mar 11 22:27:40 PDT 2012

> One interesting detail is that it is necessary to change the
> fundamental variables, because I do not have expressions for the jumps
> in velocity.  To that end, I use the augmented velocity, which is the
> ordinary velocity multiplied by the viscosity.

That may be in analogy to the mixed Laplace formulation: when you have
   - div k(x) grad p = f
then the mixed formulation is
   k^{-1} u + grad p = 0
   - div u = 0
and not
   u + k grad p = 0
   - div u = 0
The former leads to a reasonable error bound whereas the latter leads to 
a system where the error grows proportional to
   max k(x) / min k(x)
The same would be true when rewriting things as
   u + grad p = 0
   - div k u = f


Wolfgang Bangerth               email:            bangerth at math.tamu.edu
                                 www: http://www.math.tamu.edu/~bangerth/

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