A posteriori Variational Multiscale Methods for the 1D convection-diffusion equations
The present work is a continuation of a paper presented by the two first authors in the proceedings of the “Computational Science for the $21^{\rm st}$ century” conference held in Tours in 1997 honouring the $60^{\rm th}$ birthday of Roland Glowinski. It is devoted to the solution of 1D convection-d...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2023-06-01
|
| Series: | Comptes Rendus. Mécanique |
| Subjects: | |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.187/ |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | The present work is a continuation of a paper presented by the two first authors in the proceedings of the “Computational Science for the $21^{\rm st}$ century” conference held in Tours in 1997 honouring the $60^{\rm th}$ birthday of Roland Glowinski. It is devoted to the solution of 1D convection-diffusion equations in dominant convection regime situations. In that paper, an “a posteriori” VMS filtering technique was introduced. We present an extension of this technique to nonlinear convection-diffusion equations (a traffic model), providing an efficient method for the resolution of shocks from just the Galerkin solution at targeted times. We also present a residual-based “a posteriori” VMS filtering, that provides quite accurate stable solutions, can be extended to multi-dimensional problems, and can be applied locally. We finally present some numerical tests exhibiting the high accuracy of the obtained solutions. |
|---|---|
| ISSN: | 1873-7234 |