$hp$-FEM for reaction-diffusion equations II. Robust exponential convergence for multiple length scales in corner domains
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2020
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916334352203776 |
|---|---|
| author | Banjai, Lehel Melenk, Jens M. Schwab, Christoph |
| author_facet | Banjai, Lehel Melenk, Jens M. Schwab, Christoph |
| contents | In bounded, polygonal domains $Ω\subset \mathbb{R}^2$ with Lipschitz boundary $\partialΩ$ consisting of a finite number of Jordan curves admitting analytic parametrizations, we analyze $hp$-FEM discretizations of linear, second order, singularly perturbed reaction diffusion equations on so-called geometric boundary layer meshes. We prove, under suitable analyticity assumptions on the data, that these $hp$-FEM afford exponential convergence in the natural "energy" norm of the problem, as long as the geometric boundary layer mesh can resolve the smallest length scale present in the problem. Numerical experiments confirm the robust exponential convergence of the proposed $hp$-FEM. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2004_10517 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | $hp$-FEM for reaction-diffusion equations II. Robust exponential convergence for multiple length scales in corner domains Banjai, Lehel Melenk, Jens M. Schwab, Christoph Numerical Analysis 65N30, 65N12 In bounded, polygonal domains $Ω\subset \mathbb{R}^2$ with Lipschitz boundary $\partialΩ$ consisting of a finite number of Jordan curves admitting analytic parametrizations, we analyze $hp$-FEM discretizations of linear, second order, singularly perturbed reaction diffusion equations on so-called geometric boundary layer meshes. We prove, under suitable analyticity assumptions on the data, that these $hp$-FEM afford exponential convergence in the natural "energy" norm of the problem, as long as the geometric boundary layer mesh can resolve the smallest length scale present in the problem. Numerical experiments confirm the robust exponential convergence of the proposed $hp$-FEM. |
| title | $hp$-FEM for reaction-diffusion equations II. Robust exponential convergence for multiple length scales in corner domains |
| topic | Numerical Analysis 65N30, 65N12 |
| url | https://arxiv.org/abs/2004.10517 |