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 > ------------------------------------------------------------------------------ Comprehensive Server Monitoring with Site24x7. Monitor 10 servers for $9/Month. Get alerted through email, SMS, voice calls or mobile push notifications. Take corrective actions from your mobile device. http://p.sf.net/sfu/Zoho _______________________________________________ Libmesh-users mailing list [email protected] https://lists.sourceforge.net/lists/listinfo/libmesh-users
