Hello Xujun,
For the mixed FEM formulation, the pressure usually lies
in the L2 function space, whereas the velocity lies in the H1 function
space. These function spaces dictate the norm to be used for measuring the
error in the variable.
The patch recovery estimator assumes an H1 error norm, and would need to be
told that it should use L2 for the pressure variable. Can you tell us what
the code is for building your patch recovery error estimator, I can then
tell you the necessary modifications.
Thanks.
On Mon, Oct 20, 2014 at 5:16 PM, Xujun Zhao <[email protected]> wrote:
> 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
>
--
Vikram Garg
Postdoctoral Associate
Center for Computational Engineering
Massachusetts Institute of Technology
http://web.mit.edu/vikramvg/www/
http://www.runforindia.org/runners/vikramg
------------------------------------------------------------------------------
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
