A fractional Laplace equation : Regularity of solutions and finite element approximations.
Resumen:
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 Hölder 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.
| 2016 | |
| Este trabajo ha sido financiado parcialmente por CONICET bajo el programa PIP 2014-2016 11220130100184CO. | |
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Fractional Laplacian Finite elements Weighted fractional norms Graded meshes |
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| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/47831 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
