On diagonal dominance of FEM stiffness matrix of fractional Laplacian and maximum principle preserving schemes for the fractional Allen-Cahn equation

DOI10.1007/s10915-020-01363-1zbMath1473.65207arXiv2007.08183OpenAlexW3121070290MaRDI QIDQ2027967

Huifang Yuan, Li-Lian Wang, Hongyan Liu, Chang-Tao Sheng

Publication date: 28 May 2021

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.08183

zbMATH Keywords

maximum principlediagonal dominanceintegral fractional Laplacianfractional-in-space Allen-Cahn equation

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Maximum principles in context of PDEs (35B50) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Interpolation in approximation theory (41A05) Rate of convergence, degree of approximation (41A25) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58) Toeplitz, Cauchy, and related matrices (15B05) Fractional partial differential equations (35R11)

Related Items (3)

Simple positivity-preserving nonlinear finite volume scheme for subdiffusion equations on general non-conforming distorted meshes ⋮ Analytical and numerical dissipativity for the space-fractional Allen-Cahn equation ⋮ Fast \(Q1\) finite element for two-dimensional integral fractional Laplacian

Uses Software

• DLMF

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