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...
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2017
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361429_v55_n2_p472_Acosta http://hdl.handle.net/20.500.12110/paper_00361429_v55_n2_p472_Acosta |
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paper:paper_00361429_v55_n2_p472_Acosta2023-06-08T15:02:00Z A fractional Laplace equation: Regularity of solutions and finite element approximations Finite elements Fractional Laplacian Graded meshes Weighted fractional norms Integrodifferential equations Laplace equation Laplace transforms Nonlinear equations Poisson equation A-priori estimates Finite element approximations Fractional Laplacian Graded meshes Linear finite elements Optimal order of convergence Regularity of solutions Weighted fractional norms Finite element method 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. © by SIAM 2017. 2017 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361429_v55_n2_p472_Acosta http://hdl.handle.net/20.500.12110/paper_00361429_v55_n2_p472_Acosta |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Finite elements Fractional Laplacian Graded meshes Weighted fractional norms Integrodifferential equations Laplace equation Laplace transforms Nonlinear equations Poisson equation A-priori estimates Finite element approximations Fractional Laplacian Graded meshes Linear finite elements Optimal order of convergence Regularity of solutions Weighted fractional norms Finite element method |
| spellingShingle |
Finite elements Fractional Laplacian Graded meshes Weighted fractional norms Integrodifferential equations Laplace equation Laplace transforms Nonlinear equations Poisson equation A-priori estimates Finite element approximations Fractional Laplacian Graded meshes Linear finite elements Optimal order of convergence Regularity of solutions Weighted fractional norms Finite element method A fractional Laplace equation: Regularity of solutions and finite element approximations |
| topic_facet |
Finite elements Fractional Laplacian Graded meshes Weighted fractional norms Integrodifferential equations Laplace equation Laplace transforms Nonlinear equations Poisson equation A-priori estimates Finite element approximations Fractional Laplacian Graded meshes Linear finite elements Optimal order of convergence Regularity of solutions Weighted fractional norms Finite element method |
| description |
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. © by SIAM 2017. |
| title |
A fractional Laplace equation: Regularity of solutions and finite element approximations |
| title_short |
A fractional Laplace equation: Regularity of solutions and finite element approximations |
| title_full |
A fractional Laplace equation: Regularity of solutions and finite element approximations |
| title_fullStr |
A fractional Laplace equation: Regularity of solutions and finite element approximations |
| title_full_unstemmed |
A fractional Laplace equation: Regularity of solutions and finite element approximations |
| title_sort |
fractional laplace equation: regularity of solutions and finite element approximations |
| publishDate |
2017 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361429_v55_n2_p472_Acosta http://hdl.handle.net/20.500.12110/paper_00361429_v55_n2_p472_Acosta |
| _version_ |
1768544357831409664 |