A PDE approach to fractional diffusion: A posteriori error analysis

Chen, Long; Nochetto, Ricardo H.; Otarola, Enrique; Salgado, Abner J.

Abstract

We derive a computable a posteriori error estimator for the alpha-harmonic extension problem, which localizes the fractional powers of elliptic operators supplemented with Dirichlet boundary conditions. Our a posteriori error estimator relies on the solution of small discrete problems on anisotropic cylindrical stars. It exhibits built-in flux equilibration and is equivalent to the energy error up to data oscillation, under suitable assumptions. We design a simple adaptive algorithm and present numerical experiments which reveal a competitive performance. (C) 2015 Elsevier Inc. All rights reserved.

Más información

Título según WOS: ID WOS:000354119500025 Not found in local WOS DB
Título de la Revista: JOURNAL OF COMPUTATIONAL PHYSICS
Volumen: 293
Editorial: ACADEMIC PRESS INC ELSEVIER SCIENCE
Fecha de publicación: 2015
Página de inicio: 339
Página final: 358
DOI:

10.1016/j.jcp.2015.01.001

Notas: ISI