The Dual Characteristic-Galerkin Method
The Dual Characteristic-Galerkin method (DCGM) is conservative, precise and experimentally positive. We present the method and prove convergence and $L^2$-stability in the case of Neumann boundary conditions. In a 2D numerical finite element setting (FEM), the method is compared to Primal Characteri...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2024-11-01
|
| Series: | Comptes Rendus. Mathématique |
| Subjects: | |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.598/ |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1825206183035666432 |
|---|---|
| author | Hecht, Frédéric Pironneau, Olivier |
| author_facet | Hecht, Frédéric Pironneau, Olivier |
| author_sort | Hecht, Frédéric |
| collection | DOAJ |
| description | The Dual Characteristic-Galerkin method (DCGM) is conservative, precise and experimentally positive. We present the method and prove convergence and $L^2$-stability in the case of Neumann boundary conditions. In a 2D numerical finite element setting (FEM), the method is compared to Primal Characteristic-Galerkin (PCGM), Streamline upwinding (SUPG), the Dual Discontinuous Galerkin method (DDG) and centered FEM without upwinding. DCGM is difficult to implement numerically but, in the numerical context of this note, it is far superior to all others. |
| format | Article |
| id | doaj-art-bffe5f1f6cb346aaa46d1c7ef2f38198 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-bffe5f1f6cb346aaa46d1c7ef2f381982025-02-07T11:23:31ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-11-01362G101109111910.5802/crmath.59810.5802/crmath.598The Dual Characteristic-Galerkin MethodHecht, Frédéric0Pironneau, Olivier1LJLL, Boite 187, Sorbonne Université, Place Jussieu, 75005 Paris, FranceLJLL, Boite 187, Sorbonne Université, Place Jussieu, 75005 Paris, FranceThe Dual Characteristic-Galerkin method (DCGM) is conservative, precise and experimentally positive. We present the method and prove convergence and $L^2$-stability in the case of Neumann boundary conditions. In a 2D numerical finite element setting (FEM), the method is compared to Primal Characteristic-Galerkin (PCGM), Streamline upwinding (SUPG), the Dual Discontinuous Galerkin method (DDG) and centered FEM without upwinding. DCGM is difficult to implement numerically but, in the numerical context of this note, it is far superior to all others.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.598/Partial differential equationsconvection-diffusionnumerical methodfinite element method |
| spellingShingle | Hecht, Frédéric Pironneau, Olivier The Dual Characteristic-Galerkin Method Comptes Rendus. Mathématique Partial differential equations convection-diffusion numerical method finite element method |
| title | The Dual Characteristic-Galerkin Method |
| title_full | The Dual Characteristic-Galerkin Method |
| title_fullStr | The Dual Characteristic-Galerkin Method |
| title_full_unstemmed | The Dual Characteristic-Galerkin Method |
| title_short | The Dual Characteristic-Galerkin Method |
| title_sort | dual characteristic galerkin method |
| topic | Partial differential equations convection-diffusion numerical method finite element method |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.598/ |
| work_keys_str_mv | AT hechtfrederic thedualcharacteristicgalerkinmethod AT pironneauolivier thedualcharacteristicgalerkinmethod AT hechtfrederic dualcharacteristicgalerkinmethod AT pironneauolivier dualcharacteristicgalerkinmethod |