Convergence of finite difference methods for convection--diffusion problems with singular solutions

DOI10.1016/S0377-0427(02)00700-8zbMath1018.65110MaRDI QIDQ1872934

Qing Fang

Publication date: 19 May 2003

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

zbMATH Keywords

numerical examplesfinite difference methodsinitial-boundary value problemssingular solutionsconvection-diffusion equationsacceleration of convergenceShortley-Weller approximation

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Initial value problems for second-order parabolic equations (35K15)

Related Items (5)

The convergence rate for difference approximations to fractional boundary value problems ⋮ A new finite difference representation for Poisson's equation on \(\mathbb R^3\) from a contour integral ⋮ Local boundary element based a new finite difference representation for Poisson equations ⋮ Superconvergence of solution derivatives of the Shortley-Weller difference approximation to Poisson's equation with singularities on polygonal domains ⋮ Superconvergence of Solution Derivatives of the Shortley–Weller Difference Approximation to Elliptic Equations with Singularities Involving the Mixed Type of Boundary Conditions

Cites Work

• Numerical solution of partial differential equations. Transl. from the German by Peter R. Wadsack
• Geometric theory of semilinear parabolic equations
• 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
• Convergence of consistent and inconsistent finite difference schemes and an acceleration technique
• 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
• Iterative Solution Methods
• A Simple Adaptive Grid Method in Two Dimensions
• Superconvergence of finite difference approximations for convection-diffusion problems
• Convergence of swartztrauber-sweets approximation for the poisson-type equation on a disk
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