Name
Title | ||
|---|---|---|
High order symmetric direct discontinuous Galerkin method for elliptic interface problems with fitted mesh |
Abstract | ||
|---|---|---|
In this article, we aim to develop a high order symmetric direct discontinuous Galerkin method solving elliptic interface problems with zero or non-zero solution jump and flux jump interface conditions. We focus on the case, in which the mesh is partitioned along the curved interface. The two interface jump conditions are naturally and simultaneously built into the numerical flux definition on the curved triangular elements' edges that overlap with the interface. We obtain a stable and high order method, regardless of the combination of the two interface jump conditions. The two interface jump conditions are both weakly enforced in the scheme formulation. Optimal (k+1)th order L2 norm error estimate is proved for polygonal interfaces. A sequence of numerical examples is carried out to verify the optimal convergence of the symmetric direct discontinuous Galerkin method with high order P2, P3 and P4 approximations. Uniform optimal convergence order, which is independent of the diffusion coefficient ratio inside and outside of the interface, is obtained. The symmetric direct discontinuous Galerkin method is shown to be capable of handling interface problems with complicated geometries. |
Year | DOI | Venue |
|---|---|---|
2020 | 10.1016/j.jcp.2020.109301 | Journal of Computational Physics |
Keywords | DocType | Volume |
Direct discontinuous Galerkin method,Elliptic interface problem | Journal | 409 |
ISSN | Citations | PageRank |
0021-9991 | 0 | 0.34 |
References | Authors | |
0 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Hongying Huang | 1 | 0 | 0.34 |
| Jin Li | 2 | 0 | 0.34 |
| Jue Yan | 3 | 198 | 24.23 |