Finite element approximations of the nonhomogeneous fractional Dirichlet problem.
Resumen:
We study finite element approximations of the nonhomogeneous Dirichlet problem for the fractional Laplacian. Our approach is based on weak imposition of the Dirichlet condition and incorporating a nonlocal analogue of the normal derivative as a Lagrange multiplier in the formulation of the problem. In order to obtain convergence orders for our scheme, regularity estimates are developed both for the solution and for its nonlocal derivative. The method we propose requires that, as meshes are refined, the discrete problems be solved in a family of domains of growing diameter.
| 2017 | |
| Con apoyo de CONICYT-Chile a través del proyecto Fondecyt 1150056 y de CONICET bajo el fondo PIP 2014-2016 11220130100184CO. | |
|
Fractional Laplacian Mixed finite elements A priori error analysis |
|
| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/47835 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
