Super-convergence in maximum norm of the gradient for the Shortley-Weller method

DOI10.1007/s10915-017-0548-yzbMath1404.65219OpenAlexW2602058636MaRDI QIDQ1635860

Lisl Weynans

Publication date: 1 June 2018

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

Full work available at URL: https://doi.org/10.1007/s10915-017-0548-y

zbMATH Keywords

finite-differencePoisson equationdiscrete Green's functionsuper-convergenceShortley-Weller method

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Maximum principles in context of PDEs (35B50) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Finite difference methods for boundary value problems involving PDEs (65N06) Fundamental solutions, Green's function methods, etc. for boundary value problems involving PDEs (65N80)

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Cites Work

• Convergence analysis of the standard central finite difference method for Poisson equation
• Analyses on the finite difference method by gibou et al. for Poisson equation
• On the supraconvergence of elliptic finite difference schemes
• Superconvergence of the Shortley-Weller approximation for Dirichlet problems
• Superconvergence of solution derivatives for the Shortley--Weller difference approximation of Poisson's equation. I: Smoothness problems
• Superconvergence of solution derivatives of the Shortley-Weller difference approximation to Poisson's equation with singularities on polygonal domains
• Discrete maximum principle for finite-difference operators
• A REVIEW OF THE SUPRA-CONVERGENCES OF SHORTLEY-WELLER METHOD FOR POISSON EQUATION