A fractional Laplace equation: Regularity of solutions and finite element approximations
This paper deals with the integral version of the Dirichlet homogeneous fractional Laplace equation. For this problem weighted and fractional Sobolev a priori estimates are provided in terms of the Holder regularity of the data. By relying on these results, optimal order of convergence for the stand...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2017 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/55515 |
| Acceso en línea: | http://hdl.handle.net/11336/55515 |
| Access Level: | acceso abierto |
| Palabra clave: | FINITE ELEMENTS FRACTIONAL LAPLACIAN GRADED MESHES WEIGHTED FRACTIONAL NORMS https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | This paper deals with the integral version of the Dirichlet homogeneous fractional Laplace equation. For this problem weighted and fractional Sobolev a priori estimates are provided in terms of the Holder regularity of the data. By relying on these results, optimal order of convergence for the standard linear finite element method is proved for quasi-uniform as well as graded meshes. Some numerical examples are given showing results in agreement with the theoretical predictions. |
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