Convergence of consistent and inconsistent finite difference schemes and an acceleration technique

DOI10.1016/S0377-0427(01)00522-2zbMath1004.65107MaRDI QIDQ1602821

Tetsuro Yamamoto

Publication date: 24 June 2002

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

numerical exampleDirichlet problemssuperconvergencefinite difference methodsacceleration of convergenceinconsistent scheme

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)

Related Items (9)

Convergence of finite difference methods for convection--diffusion problems with singular solutions ⋮ Convergence Analysis of the Shortley-Weller Method on Refinement Grids for Elliptic Equations with Singularities ⋮ The convergence rate for difference approximations to fractional boundary value problems ⋮ Convergence of the Swartztrauber-Sweet Method for Parabolic Problems on a Disk with Singularities ⋮ Superconvergence of solution derivatives of the Shortley-Weller difference approximation to Poisson's equation with singularities on polygonal domains ⋮ Nonuniform FDM for Poisson-Type Equations on a Disk with Singular Solutions ⋮ Superconvergence of Solution Derivatives for the Shortley–Weller Difference Approximation of Poisson's Equation. II. Singularity Problems ⋮ Error Analysis of Adaptive Finite Difference Methods Using Stretching Functions for Polar Coordinate Form of Poisson-Type Equation ⋮ Superconvergence of Solution Derivatives of the Shortley–Weller Difference Approximation to Elliptic Equations with Singularities Involving the Mixed Type of Boundary Conditions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Numerical solution of partial differential equations. Transl. from the German by Peter R. Wadsack
• Numerical analysis of blood flow in the heart
• Analysis of difference approximations to a singularly perturbed two-point boundary value problem on an adaptively generated grid
• Superconvergence of the Shortley-Weller approximation for Dirichlet problems
• Superconvergence in Galerkin finite element methods
• Numerical solution of a singularly perturbed two-point boundary value problem using equidistribution: Analysis of convergence
• On the formulation of finite difference analogues of the Dirichlet problem for Poisson's equation
• SUPERCONVERGENCE AND NONSUPERCONVERGENCE OF THE SHORTLEY-WELLER APPROXIMATIONS FOR DIRICHLET PROBLEMS
• A Study of Monitor Functions for Two-Dimensional Adaptive Mesh Generation
• A Simple Adaptive Grid Method in Two Dimensions
• The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
• Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension
• Superconvergence of finite difference approximations for convection-diffusion problems

This page was built for publication: Convergence of consistent and inconsistent finite difference schemes and an acceleration technique