Constructive approximation on graded meshes for the integral fractional Laplacian.
Resumen:
We consider the homogeneous Dirichlet problem for the integral fractional Laplacian (−Δ)s. We prove optimal Sobolev regularity estimates in Lipschitz domains provided the solution is Cs up to the boundary. We present the construction of graded bisection meshes by a greedy algorithm and derive quasi-optimal convergence rates for approximations to the solution of such a problem by continuous piecewise linear functions. The nonlinear Sobolev scale dictates the relation between regularity and approximability.
| 2022 | |
| Juan Pablo Borthagaray ha sido apoyado en parte por la beca Fondo Vaz Ferreira 2019-068. | |
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Integral fractional Laplacian Graded Meshes Greedy algorithm |
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| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/47711 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
