\({\mathscr{H}} \)-matrix approximability of inverses of discretizations of the fractional Laplacian
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Publication:2305555
DOI10.1007/s10444-019-09718-5zbMath1435.65205arXiv1808.04274OpenAlexW2987877651MaRDI QIDQ2305555
Jens Markus Melenk, Michael Karkulik
Publication date: 11 March 2020
Published in: Advances in Computational Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1808.04274
Computational methods for sparse matrices (65F50) Fractional derivatives and integrals (26A33) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Direct numerical methods for linear systems and matrix inversion (65F05) Fractional partial differential equations (35R11)
Related Items (17)
Caccioppoli-type estimates and \(\mathcal{H}\)-matrix approximations to inverses for FEM-BEM couplings ⋮ Tensor product method for fast solution of optimal control problems with fractional multidimensional Laplacian in constraints ⋮ Weighted Analytic Regularity for the Integral Fractional Laplacian in Polygons ⋮ Local Convergence of the FEM for the Integral Fractional Laplacian ⋮ A reduced basis method for fractional diffusion operators. I ⋮ Finite element discretizations for variable-order fractional diffusion problems ⋮ Exponential Convergence of \(hp\)-FEM for the Integral Fractional Laplacian in Polygons ⋮ Exponential convergence of \textit{hp} FEM for spectral fractional diffusion in polygons ⋮ Analysis of a sinc-Galerkin Method for the Fractional Laplacian ⋮ Robust BPX preconditioner for fractional Laplacians on bounded Lipschitz domains ⋮ Fractional elliptic problems on Lipschitz domains: regularity and approximation ⋮ Finite element methods for fractional-order diffusion problems with optimal convergence order ⋮ Numerical approximations for a fully fractional Allen–Cahn equation ⋮ A reduced basis method for fractional diffusion operators. II ⋮ Quasi-optimal convergence rate for an adaptive method for the integral fractional Laplacian ⋮ Linear and nonlinear fractional elliptic problems ⋮ Space-fractional diffusion with variable order and diffusivity: discretization and direct solution strategies
Uses Software
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