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. > What exact solution are you using for testing the convergence? > > > I am considering adding higher order quads to get x- and > > y- interpolation using higher-order Lagrange functions. Any thoughts on > how > > easy/difficult this might be? > > You are talking about QUAD16? It shouldn't be too hard but we would > need to come to a consesus on node numbering for this element. > > 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. -Manav ------------------------------------------------------------------------------ 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
