[CIG-CS] Sinker example in Matlab

[Wolfgang Bangerth]

> One benchmark that they did was a circular inclusion under pure shear.
> This usually has the same problem as we saw with the sinking block
> benchmark, where there are consistent overshoots and undershoots of
> the pressure near the material interface.
> 
> However, Duretz et. al.  claimed to get a convergent solution, so I
> thought that they might have gotten around this issue.  Reading the
> paper, the only difference that I could see that really matters
> between my finite difference code and theirs is that they used a
> direct solver.
> 
> Modifying my code to use a direct solver would be difficult.
> Fortunately, as part of Taras Gerya's book, he also distributes Matlab
> code that solves Stokes using finite differences and a direct solver.
> He even solves a version of the sinker benchmark.  So I was able to
> modify that to reproduce the form of the sinker benchmark that I had
> applied to the deal.II and Samrai codes.  I have attached a picture
> showing the instantaneous solution for the pressure.
> 
> I still see the overshoot and undershoot.  So I am not sure what is
> going on with Duretz et. al.

I'd say ask them. 

Certainly, the question of solver should not affect the solution -- if an 
iterative solver produces spikes the direct solver does not produce, then the 
iteratively generated solution is wrong, and the conclusions thus drawn about 
the discretization are too. But since you get the same results for both 
solvers, you should be on the safe side.

Best
 W.

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