On Tue, May 14, 2013 at 11:54 AM, Manav Bhatia <[email protected]> wrote: > > > On Tue, May 14, 2013 at 12:59 PM, John Peterson <[email protected]> > wrote: >> >> On Tue, May 14, 2013 at 9:25 AM, Manav Bhatia <[email protected]> >> wrote: >> > Hi, >> > >> > I am working on higher-order simulation using the hierarchich >> > function >> > on quad8s. >> > >> > My error-convergence plots give me theoretical convergence for first >> > and second order p, but the error stagnates for p > 2. I am speculating >> > that this might be due to the lower-order geometry, assuming that the x- >> > and y-coordinates are interpolated using Lagrange functions associated >> > with >> > nodes of quad8. >> >> What does your domain look like? Unit square? If so I don't think >> there can be errors due to using even bilinear element maps, the >> Jacobians are linear in this case. >> > > This is the Gaussian bump problem from the higher-order CFD workshop > (http://dept.ku.edu/~cfdku/hiocfd/case_c1.1.html). You are correct that away > from the bump the boundary is straight, so linear elements should be fine. I > am looking at the entropy error, since the entropy is supposed to stay > constant. The bump-boundary, infact, is adding to the entropy-error. I am > able to drop down to 10^-7 in the error L2 norm, and then it stagnates. And > I have a feeling that this is due to the low-order geometry.
Oh yeah, I have heard of this spurious entropy production problem on curved geometries. Are you really using Quad8's? Can you use Quad9's with the hierarchics? Can you modify the test problem slightly so the bump is a quadratic function and verify convergence with higher p's? > Yes, I was considering this, and also the 25-noded quad. However, I am still > considering if the effort might be worth it: Meaning that I may be able to > get theoretical order of convergence for this simpler benchmark problem, but > I don't know if any practical problem will benefit from a 16 or 25 noded > quad. I am not sure if any mesh generator would give me elements with these > many nodes. You will probably have trouble viewing the solutions in Paraview too... -- John ------------------------------------------------------------------------------ AlienVault Unified Security Management (USM) platform delivers complete security visibility with the essential security capabilities. Easily and efficiently configure, manage, and operate all of your security controls from a single console and one unified framework. Download a free trial. http://p.sf.net/sfu/alienvault_d2d _______________________________________________ Libmesh-users mailing list [email protected] https://lists.sourceforge.net/lists/listinfo/libmesh-users
