[CIG-CS] Sinker example in Matlab + discretisation errors of the staggered grid FD method for variable viscosity stokes

[Wolfgang Bangerth]

> Does that mean that the L_infinity norm for the inclusion test does
> not converge?

That wouldn't be surprising for problems where the solution is 
essentially discontinuous. The same is true, for example, if you try to 
approximate a discontinuous function with a finite Fourier series: it 
converges in L2 and L1, but not L_infinity.

There is nothing you can do about that -- it's called Gibb's phenomenon. 
I would almost want to venture the guess that that is a property that's 
common to pretty much any other basis as well, including any finite 
element basis.


> This is something that puzzled me for a while.  For many equations, it
> is difficult to come up with a scheme that is L1 convergent but not
> L_infinity convergent.  That does not seem to be the case for Stokes.

I think it is actually the other way around. On a finite domain, you have

   ||e||_{L1}  <=  size of domain * ||e||_{L_infinity}

so whatever is Linfinity-convergent must also be L1 convergent. (Unless 
I read your sentence as saying that it's difficult to come up with 
pathological discretizations that do converge in L1 but not in Linfinity 
-- this would indeed be difficult for something like the Laplace equation.)

Best
W.