Timeline for Advection equation using the finite element method
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 27, 2015 at 14:36 | comment | added | Bill Barth | That probably should have said "typically don't" rather than "can't". I've subsequently found papers doing so after not trusting myself. | |
| Sep 27, 2015 at 13:30 | comment | added | Bill Barth | @Justin, even though you can't derive the weak form for the FEM method for the convection-diffusion equation as the first-order optimality equation of some functional, you can add a Lagrange multiplier as though you had. A term like $\int \lambda (c-c_0) \; dx$ will keep $c$ away from $c_0$ where this term comes from the KKT conditions for minimizing $ 0.5\int (c-c_0)^2 \; dx $. I haven't tried this in the pure convection context, but it works fine to prevent spurious oscillations in the convection-diffusion problem. | |
| Sep 27, 2015 at 9:22 | comment | added | Justin | @BillBarth can you elaborate on this a little more? I know it's now going off topic so I can create another thread if necessary | |
| Sep 24, 2015 at 23:18 | comment | added | Bill Barth | I can't say anything about the mathematics, but you can prevent negative solution oscillations with a penalty in a Galerkin method. I never published anything on it, but I have tried it successfully. | |
| Sep 24, 2015 at 18:39 | vote | accept | Justin | ||
| Sep 24, 2015 at 18:39 | comment | added | Justin | Okay, I guess I will just give it a try then. Thanks | |
| Sep 24, 2015 at 12:50 | comment | added | Wolfgang Bangerth | I don't know. It's certainly possible to try something like this. It's a different question whether it works. | |
| Sep 23, 2015 at 23:11 | comment | added | Justin | Thanks for the link to the video, what you say makes sense. It seems to me that LSFEM without any stabilization exhibits the same "oscillations" as the SUPG formulation. That is, my solution violates the Discrete Maximum Principles and is not monotonic everywhere. Unlike SUPG, LSFEM is naturally an unconstrained minimization/optimization problem so could I enforce bounded/inequality constraints to "fix" my solution? Would this be mathematically sound? | |
| Sep 23, 2015 at 14:36 | history | answered | Wolfgang Bangerth | CC BY-SA 3.0 |