A PDE approach to fractional diffusion: a posteriori error analysis
Numerical Analysis
2015-05-20 v2
Abstract
We derive a computable a posteriori error estimator for the -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.
Keywords
Cite
@article{arxiv.1406.2281,
title = {A PDE approach to fractional diffusion: a posteriori error analysis},
author = {Long Chen and Ricardo H. Nochetto and Enrique Otárola and Abner J. Salgado},
journal= {arXiv preprint arXiv:1406.2281},
year = {2015}
}