Convergence analysis of the standard central finite difference method for Poisson equation

DOI10.1007/s10915-015-0096-2zbMath1345.65063OpenAlexW1795310201MaRDI QIDQ292556

Chohong Min, Gang Joon Yoon

Publication date: 8 June 2016

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

Full work available at URL: https://doi.org/10.1007/s10915-015-0096-2

zbMATH Keywords

convergencefinite difference methodPoisson equationnumerical testdiscrete divergence theorem

Mathematics Subject Classification ID

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)

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Cites Work

• Analyses on the finite difference method by gibou et al. for Poisson equation
• Guidelines for Poisson solvers on irregular domains with Dirichlet boundary conditions using the ghost fluid method
• An efficient fluid-solid coupling algorithm for single-phase flows
• Superconvergence of the Shortley-Weller approximation for Dirichlet problems
• A second-order-accurate symmetric discretization of the Poisson equation on irregular domains
• Convergence analysis on the Gibou-Min method for the Hodge projection
• Superconvergence of solution derivatives of the Shortley-Weller difference approximation to Poisson's equation with singularities on polygonal domains
• Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface
• A First Course in the Numerical Analysis of Differential Equations
• Superconvergence of Solution Derivatives for the Shortley–Weller Difference Approximation of Poisson's Equation. II. Singularity Problems
• A REVIEW OF THE SUPRA-CONVERGENCES OF SHORTLEY-WELLER METHOD FOR POISSON EQUATION
• The Numerical Solution of Laplace's Equation
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