Functional a posteriori estimates for the fractional Laplacian problem

Alexander Nazarov; Sergey Repin

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arXiv · 2510.12664

Functional a posteriori estimates for the fractional Laplacian problem

Alexander Nazarov·Sergey Repin

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Abstract

The paper is concerned with a posteriori estimates for approximations of boundary value problems generated by the spectral fractional Laplace operator. The derivation is based upon the Stinga--Torrea extension, which generalizes the Caffarelli--Silvestre extension and transfers the corresponding nonlocal problem in a bounded domain to a local problem of higher dimensionality. A posteriori estimates are first derived for this local problem. Two-sided error bounds for the original problem follow from them. The estimates are fully computable and contain no conditions and constants depending on a method or mesh used to compute an approximation. They are valid for any energy admissible approximation of the extended problem.

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Alexander Nazarov, Sergey Repin. 2025-10-14. Functional a posteriori estimates for the fractional Laplacian problem. https://arxiv.org/abs/2510.12664

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