Published

A PDE approach to fractional diffusion: a posteriori error analysis

L Chen, RH Nochetto, E Otarola, AJ Salgado

Journal of Computational Physics, 293, 339-358, 2015

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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.