The true solution, u has 1/r singularity and pressure should have 1/r^2
singularity. So probably this is the case for singular problems, such as
cracks.

Yes, I limited the time of refinement in each element below 10 to make it
stop. But the problem is that if the results do not converge, how can I
trust my numerical results? is this the reason why 1/4 mid-point singular
element is used in cracks?

Xujun

Xujun

On Mon, Oct 20, 2014 at 5:07 PM, John Peterson <[email protected]> wrote:

> On Mon, Oct 20, 2014 at 3:31 PM, Xujun Zhao <[email protected]> wrote:
> > Hi all,
> >
> > For adaptive mesh refinement, an error estimator has to be used to
> > approximately evaluate the errors in each element in order to determine
> > which element is going to be refined. My question is which error
> estimator
> > should be used in the mixed FEM formulations, for example, Stokes
> equation
> > with u-p formulation. I read Bathe KJ's review paper:
> > A posteriori error estimation techniques in practical finite element
> > analysis, Computer & Structures 2005 p 235-265.
> > in which they suggested another local error indicator.
> >
> > I did try kelly and patch recovery, and they are useful to locate the
> > singular region and refine the mesh near the singularity. But the error
> > norms become larger and larger with the refinement. It seems that the
> > numerical solution is not convergent with mesh refinement.
>
> Is your true solution (especially for pressure) in H1?
>
> If not, like for the non-leaky lid-driven cavity, then Kelly will keep
> giving you larger and larger error estimates.
>
> In practice, you can limit the amount of refinement in the singularity
> by calling max_h_level() on the MeshRefinement object.
>
> --
> John
>
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