A PDE approach to fractional diffusion: A posteriori error analysis

JOURNAL OF COMPUTATIONAL PHYSICS

卷:293

Article

Chen, Long¹  Nochetto, Ricardo H.^2,3  Otarola, Enrique^2,4  Salgado, Abner J.⁵ 

[1] Univ Calif Irvine, Dept Math, Irvine, CA 92697 USA

[2] Univ Maryland, Dept Math, College Pk, MD 20742 USA

[3] Univ Maryland, Inst Phys Sci & Technol, College Pk, MD 20742 USA

[4] George Mason Univ, Dept Math Sci, Fairfax, VA 22030 USA

[5] Univ Tennessee, Dept Math, Knoxville, TN 37996 USA

关键词: Fractional diffusion;    Finite elements;    A posteriori error estimates;    Nonlocal operators;    Nonuniformly elliptic equations;    Anisotropic elements;    Adaptive algorithm;   

DOI  :  10.1016/j.jcp.2015.01.001

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free