Re: [Libmesh-users] higher order elements

[John P. <jwp...@gm...>]

On May 14, 2013, at 12:37 PM, Manav Bhatia <bha...@gm...> wrote:

>> >
>> > 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?
>  
> This is a great suggestion, John. I will try converting the geometry to second order. 
>  
> I have not tried Quad9, but what would that be any better than Quad8?

Not much other than it would have the x^2 y^2 term in its map.

One other thought:  do you have some O(h) stabilization terms present?  Then if you aren't refining the grid they don't get smaller...



>> > 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...
> As it is, I am having trouble viewing results from higher-order elements in Paraview. I can output only the nodal data for viewing in Paraview, and so the higher-order information of the element solution gets lost. I haven't yet had the chance to look into improving this behavior.
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> Roy:   Just to clarify, I do get a reduction in error for higher order elemets after 10^-7, but the rate of convergence is considerably lower than the p+1/2 theoretical order. I will try compiling with quad precision to see if that does something. I have played around with the solver parameters, and have also used direct solvers to flush out any potential problems form linear solvers.
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