Timeline for How to implement FEM for a 2D PDE with variable coefficients
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Jun 6, 2023 at 8:59 | vote | accept | Faz | ||
| Feb 15, 2021 at 3:00 | history | tweeted | twitter.com/StackMma/status/1361148257104261124 | ||
| Feb 14, 2021 at 21:02 | history | edited | Faz | CC BY-SA 4.0 |
added 154 characters in body
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| Feb 14, 2021 at 20:02 | answer | added | Alex Trounev | timeline score: 6 | |
| Feb 14, 2021 at 11:45 | comment | added | Faz | Yes, those are useless somehow. But can you solve via FEM methodology in any way and get a final solution curve and the value at (100,0.04)? If you can obtain good numerical accuracy with FEM (in any format), please write it as a response. | |
| Feb 13, 2021 at 22:03 | comment | added | Alex Trounev |
Boundary conditions at infinity look useless. We can try to solve problem without boundary conditions, only with initial data as Monitor[lines = NDSolve[{eqns, initc}, U[t], {t, 0, TT}, EvaluationMonitor :> (monitor = Row[{"t = ", CForm[t]}])], monitor];. Then we can try to implement bc at v=0.
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| Feb 12, 2021 at 13:08 | comment | added | Faz |
Another point is, even when I try to use NDSolve and directly solve the 2D PDE with variable coefficients and FEM, I cannot get the results easily since here there are three major boundary conditions and there is no boundary condition when $v=0$. Also, if I use an ABC such as the vanishing second derivative at this side of the domain, one more time NDSolve prints an error that cannot solve the PDE with such boundary conditions.
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| Feb 12, 2021 at 13:03 | comment | added | Faz | Please see Table 3 (Case 1) in the PDF that can be downloaded in the following link: semanticscholar.org/paper/… | |
| Feb 12, 2021 at 10:15 | comment | added | Alex Trounev | Could you give a link to the paper you mentioned above? | |
| Feb 12, 2021 at 8:28 | comment | added | Faz | We have the reference solution from a published work which says that at a specific point (100, 0.04) of the domain, the solution is 8.8948. Accordingly, after I compute the numerical solution by solving the system of linear ODEs, and save it in $f$, I can find the final error. The point here is, if we use the FD method and fill up the differentiation matrices with FD weights, the last part of the code would be similar and everything goes fine and you can see the convergence. But for the FEM, I do not know how to implement the FEM differentiation matrices to construct the final system of ODEs! | |
| Feb 11, 2021 at 22:02 | comment | added | Alex Trounev |
How you determined the the error is of 8.894869 - f[100, v0]?
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| Feb 11, 2021 at 13:01 | history | edited | Faz | CC BY-SA 4.0 |
Maybe the recent title can help to draw attentions for putting some comments
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| Feb 10, 2021 at 19:05 | history | asked | Faz | CC BY-SA 4.0 |