On the Convergence in $H^1$-Norm for the Fractional Laplacian

DOI10.1137/18M1221436zbMath1422.65371arXiv1810.07645OpenAlexW2963462097MaRDI QIDQ5232304

Juan Pablo Borthagaray, Patrick~jun. Ciarlet

Publication date: 2 September 2019

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

Full work available at URL: https://arxiv.org/abs/1810.07645

zbMATH Keywords

finite elementsgraded meshesfractional Laplacian

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Fractional partial differential equations (35R11)

Related Items (12)

A Monotone Discretization for Integral Fractional Laplacian on Bounded Lipschitz Domains: Pointwise Error Estimates under Hölder Regularity ⋮ Finite element algorithms for nonlocal minimal graphs ⋮ Local Convergence of the FEM for the Integral Fractional Laplacian ⋮ Non-local to local transition for ground states of fractional Schrödinger equations on \(\mathbb{R}^N\) ⋮ Fractional Laplacians : a short survey ⋮ Besov regularity for the Dirichlet integral fractional Laplacian in Lipschitz domains ⋮ Fractional elliptic problems on Lipschitz domains: regularity and approximation ⋮ Non-local to local transition for ground states of fractional Schrödinger equations on bounded domains ⋮ Quasi-optimal convergence rate for an adaptive method for the integral fractional Laplacian ⋮ Optimal control of fractional elliptic PDEs with state constraints and characterization of the dual of fractional-order Sobolev spaces ⋮ Linear and nonlinear fractional elliptic problems ⋮ Local Energy Estimates for the Fractional Laplacian

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