Timeline for Singularities forming on boundary while solving system of pde's
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 29, 2020 at 9:00 | history | tweeted | twitter.com/StackMma/status/1299632902616031234 | ||
| Aug 29, 2020 at 3:59 | comment | added | xzczd♦ |
Just tested in v12.0.1, the ndsz warning no longer pops up, at least in this specific example.
|
|
| Aug 29, 2020 at 3:59 | history | edited | xzczd♦ | CC BY-SA 4.0 |
added 84 characters in body
|
| Aug 29, 2020 at 3:36 | history | edited | xzczd♦ |
edited tags
|
|
| Jan 20, 2019 at 19:51 | vote | accept | Woody | ||
| Jan 18, 2019 at 16:11 | answer | added | xzczd♦ | timeline score: 7 | |
| Jan 18, 2019 at 15:38 | comment | added | Woody | @xzczd Sorry, should say "increase t0 to 3.8595/f". I've edited the question. | |
| Jan 18, 2019 at 15:37 | history | edited | Woody | CC BY-SA 4.0 |
edited body
|
| Jan 18, 2019 at 15:25 | comment | added | Woody | @HenrikSchumacher Sorry, I should have clarified. Instead of using r = 0, which I realize will introduce a singularity, I use a small value. In this case, 10^-6, to avoid any infinite expressions. Is that what you are refering to? Also, from my understanding FEM does not work for spatial derivatives with an order higher than 2. Mine has spatial derivatives up to 3. | |
| Jan 18, 2019 at 15:12 | comment | added | Henrik Schumacher |
You introduced the singularities yourself by using polar coordinates: While the actual PDE on the disk may have smooth solutions, the polar coordinates pulls this solution back to something with a singularity for $r= 0$ because the differential of the polar coordinate mapping is singular for $r=0$. So any discrete method for solving the PDE will exhibit large errors because the fundamental assumptions in all convergence proofs for discrete methods exploit that the solution of the continuous problem is smooth. I'd suggest to apply FEM (by using NDSolve) directly on the original disk.
|
|
| Jan 18, 2019 at 14:31 | history | asked | Woody | CC BY-SA 4.0 |