The direct method of lines for elliptic problems in star-shaped domains
| Autor: | Zhongyi Huang, Yi Yang, Zhizhang Wu, Wei-Cheng Wang |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Quarter period
Applied Mathematics Direct method Mathematical analysis Parameterized complexity 010103 numerical & computational mathematics Lipschitz continuity 01 natural sciences Jacobi elliptic functions 010101 applied mathematics Computational Mathematics Elliptic curve point multiplication Elliptic rational functions 0101 mathematics Schoof's algorithm Mathematics |
| Zdroj: | Journal of Computational and Applied Mathematics. 327:350-361 |
| ISSN: | 0377-0427 |
| DOI: | 10.1016/j.cam.2017.06.028 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect