Local Convergence of the FEM for the Integral Fractional Laplacian

DOI10.1137/20M1343853MaRDI QIDQ5080498

Markus Faustmann, Michael Karkulik, Jens Markus Melenk

Publication date: 31 May 2022

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

Full work available at URL: https://arxiv.org/abs/2005.14109

zbMATH Keywords

finite element methodfractional Laplacianlocal estimates

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) Numerical analysis (65-XX)

Related Items (6)

Weighted Analytic Regularity for the Integral Fractional Laplacian in Polygons ⋮ Efficient Monte Carlo Method for Integral Fractional Laplacian in Multiple Dimensions ⋮ Exponential Convergence of \(hp\)-FEM for the Integral Fractional Laplacian in Polygons ⋮ Besov regularity for the Dirichlet integral fractional Laplacian in Lipschitz domains ⋮ A Grid-Overlay Finite Difference Method for the Fractional Laplacian on Arbitrary Bounded Domains ⋮ Fractional elliptic problems on Lipschitz domains: regularity and approximation

Cites Work

• Unnamed Item
• Unnamed Item
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• Unnamed Item
• Fractional Laplacians on domains, a development of Hörmander's theory of \(\mu\)-transmission pseudodifferential operators
• Ten equivalent definitions of the fractional Laplace operator
• Localization and post processing for the Galerkin boundary element method applied to three-dimensional screen problems
• Local convergence of the boundary element method on polyhedral domains
• A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian
• Numerical approximation of the integral fractional Laplacian
• What is the fractional Laplacian? A comparative review with new results
• \({\mathscr{H}} \)-matrix approximability of inverses of discretizations of the fractional Laplacian
• Tensor FEM for spectral fractional diffusion
• A PDE approach to fractional diffusion in general domains: a priori error analysis
• Nonlinear equations for fractional Laplacians. I: Regularity, maximum principles, and Hamiltonian estimates
• A Fractional Laplace Equation: Regularity of Solutions and Finite Element Approximations
• Local energy estimates for the finite element method on sharply varying grids
• Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
• Local Error Estimates for Some Petrov-Galerkin Methods Applied to Strongly Elliptic Equations on Curves
• Interior Estimates for Ritz-Galerkin Methods
• Elliptic Partial Differential Equations of Second Order
• Hybrid Finite Element--Spectral Method for the Fractional Laplacian: Approximation Theory and Efficient Solver
• The K-Operator and the Galerkin Method for Strongly Elliptic Equations on Smooth Curves: Local Estimates
• Quasi-optimal convergence rate for an adaptive method for the integral fractional Laplacian
• Local Energy Estimates for the Fractional Laplacian
• On the Convergence in $H^1$-Norm for the Fractional Laplacian
• Numerical approximation of fractional powers of elliptic operators
• Computing Fractional Laplacians on Complex-Geometry Domains: Algorithms and Simulations
• An Extension Problem Related to the Fractional Laplacian
• Finite element approximations of the nonhomogeneous fractional Dirichlet problem
• Boundary Element Methods
• Numerical methods for fractional diffusion

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