Local Energy Estimates for the Fractional Laplacian

DOI10.1137/20M1335509zbMath1486.65240arXiv2005.03786OpenAlexW3181328114MaRDI QIDQ5001382

Dmitriy Leykekhman, Juan Pablo Borthagaray, Ricardo H. Nochetto

Publication date: 19 July 2021

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.03786

zbMATH Keywords

error estimatesfinite elementsfractional Laplacianinterior error estimates

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Fractional derivatives and integrals (26A33) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Fractional partial differential equations (35R11)

Related Items (13)

A Monotone Discretization for Integral Fractional Laplacian on Bounded Lipschitz Domains: Pointwise Error Estimates under Hölder Regularity ⋮ Local Convergence of the FEM for the Integral Fractional Laplacian ⋮ Efficient Monte Carlo Method for Integral Fractional Laplacian in Multiple Dimensions ⋮ Analysis of a sinc-Galerkin Method for the Fractional Laplacian ⋮ Discretised general fractional derivative ⋮ Robust BPX preconditioner for fractional Laplacians on bounded Lipschitz domains ⋮ Finite element approximation of optimal control problem with integral fractional Laplacian and state constraint ⋮ Error estimates for fractional semilinear optimal control on Lipschitz polytopes ⋮ Adaptive finite element approximation of optimal control problems with the integral fractional Laplacian ⋮ Fractional elliptic problems on Lipschitz domains: regularity and approximation ⋮ An a posteriori error estimator for the spectral fractional power of the Laplacian ⋮ Constructive approximation on graded meshes for the integral fractional Laplacian ⋮ Optimal control of mixed local-nonlocal parabolic PDE with singular boundary-exterior data

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