Functional a Posteriori Estimates for the Fractional Laplacian Problem
Abstract
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.
Fields of Study & Subjects
Fractional Differential Equations Solutions
Differential Equations and Boundary Problems
Nonlinear Differential Equations Analysis
Publication details
- Journal / source
- Computational Methods in Applied Mathematics
- Publisher
- Walter de Gruyter GmbH
- Volume
- 26
- Issue
- 2
- Pages
- 241–253
- Publication date
- 26 March 2026
- Language
- EN