Timeline for Usefulness of elements with mesh-dependent stability
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 18, 2016 at 21:27 | vote | accept | knl | ||
| Nov 16, 2016 at 10:18 | answer | added | Joce | timeline score: 1 | |
| Mar 4, 2016 at 8:41 | comment | added | knl | I think MINI does not have this problem. The single interior DOF will save the situation. Uniqueness condition for Stokes is $(\nabla\cdot v, p)=0~\forall v \in V_h \Rightarrow p =\text{global const.}$. Let $p(x,y)=a+bx+cy$. Choose $v=(b\phi,c\phi)$ where $\phi$ is the bubble in some tetra. This gives that $p$ is local constant and continuity takes care of the rest. | |
| Mar 4, 2016 at 0:45 | comment | added | Daniel Shapero | I wonder if this is also a problem with the MINI element? | |
| Mar 1, 2016 at 19:30 | comment | added | Christian Waluga | Interesting question! As far as I see, these elements typically result from structured tetrahedral mesh generation on cubes and such and play only a minor role in real applications where you have unstructured nodalization algorithms. I have tried a bit around a while ago and was not able to produce such a mesh with a mesh generator producing fully unstructured meshes. I suspect they employ a mechanism to avoid such over-constrained elements. I have no access to COMSOL though but I guess that for most solvers these element do not pose a significant problem. | |
| Mar 1, 2016 at 18:29 | history | tweeted | twitter.com/StackSciComp/status/704735450460790784 | ||
| Mar 1, 2016 at 16:23 | history | asked | knl | CC BY-SA 3.0 |