A PDE approach to fractional diffusion: a posteriori error analysis

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.

References in corpus (2)

• Multilevel methods for nonuniformly elliptic operators
• Piecewise polynomial interpolation in Muckenhoupt weighted Sobolev spaces and applications

Cited by in corpus (6)

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• $hp$-Finite Elements for Fractional Diffusion
• Numerical approximations for fractional elliptic equations via the method of semigroups
• An a posteriori error estimator for the spectral fractional power of the Laplacian
• On the stability of Scott-Zhang type operators and application to multilevel preconditioning in fractional diffusion
• An adaptive finite element method for the sparse optimal control of fractional diffusion