Name
Title | ||
|---|---|---|
Automatically stable discontinuous Petrov-Galerkin methods for stationary transport problems: Quasi-optimal test space norm |
Abstract | ||
|---|---|---|
We investigate the application of the discontinuous Petrov-Galerkin (DPG) finite element framework to stationary convection-diffusion problems. In particular, we demonstrate how the quasi-optimal test space norm improves the robustness of the DPG method with respect to vanishing diffusion. We numerically compare coarse-mesh accuracy of the approximation when using the quasi-optimal norm, the standard norm, and the weighted norm. Our results show that the quasi-optimal norm leads to more accurate results on three benchmark problems in two spatial dimensions. We address the problems associated to the resolution of the optimal test functions with respect to the quasi-optimal norm by studying their convergence numerically. In order to facilitate understanding of the method, we also include a detailed explanation of the methodology from the algorithmic point of view. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1016/j.camwa.2013.07.016 | Computers & Mathematics with Applications |
Keywords | Field | DocType |
coarse-mesh accuracy,algorithmic point,standard norm,weighted norm,quasi-optimal test space norm,dpg method,optimal test function,stationary transport problem,benchmark problem,quasi-optimal norm,accurate result,stable discontinuous petrov-galerkin method,numerical stability,robustness,finite element method | Convergence (routing),Mathematical optimization,Mathematical analysis,Galerkin method,Norm (social),Finite element method,Robustness (computer science),Mathematics,Numerical stability | Journal |
Volume | Issue | ISSN |
66 | 10 | 0898-1221 |
Citations | PageRank | References |
3 | 1.87 | 9 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Antti H. Niemi | 1 | 26 | 5.51 |
| Nathaniel O. Collier | 2 | 29 | 5.30 |
| Victor M. Calo | 3 | 191 | 38.14 |