Name
Abstract | ||
|---|---|---|
In this paper, we generalize the direct method of lines for elliptic problems in star-shaped domains. We assume that the boundary of the star-shaped domain is a closed Lipschitz curve that can be parameterized by the angular variable, so that an appropriate transformation of coordinates can be introduced. Then the elliptic problem is reduced to a variational–differential problem on a semi-infinite strip in the new coordinates. We discretize the reduced problem with respect to the angular variable and obtain a semi-discrete approximation. Then a direct method is adopted to solve the semi-discrete problem analytically. Finally, the optimal error estimate of the semi-discrete approximation is given and several numerical examples are presented to show that our method is feasible and effective for a wide range of elliptic problems. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1016/j.cam.2017.06.028 | Journal of Computational and Applied Mathematics |
Keywords | Field | DocType |
Elliptic problems,Star-shaped domains,Methods of lines,Finite element approximation,Semi-discrete approximation | Jacobi elliptic functions,Discretization,Elliptic rational functions,Parameterized complexity,Mathematical optimization,Mathematical analysis,Quarter period,Elliptic curve point multiplication,Lipschitz continuity,Mathematics,Schoof's algorithm | Journal |
Volume | ISSN | Citations |
327 | 0377-0427 | 0 |
PageRank | References | Authors |
0.34 | 7 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Zhizhang Wu | 1 | 0 | 0.68 |
| Zhongyi Huang | 2 | 67 | 12.67 |
| Wei-Cheng Wang | 3 | 7 | 2.80 |
| Yi Yang | 4 | 277 | 61.06 |