On a set of singularly perturbed convection--diffusion equations

DOI10.1016/j.cam.2004.10.009zbMath1073.65063OpenAlexW2116526228MaRDI QIDQ1779426

Torsten Linss

Publication date: 1 June 2005

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

Full work available at URL: https://doi.org/10.1016/j.cam.2004.10.009

zbMATH Keywords

stabilityconvergenceerror estimatesShishkin meshesSingular perturbationFinite differencesBakhvalov meshesfirst-order upwind difference schemeLayer-adapted meshesSystems of convection-diffusion equations

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Error bounds for numerical methods for ordinary differential equations (65L70) Linear boundary value problems for ordinary differential equations (34B05) Singular perturbations for ordinary differential equations (34E15) Finite difference and finite volume methods for ordinary differential equations (65L12)

Related Items (8)

Numerical simulation of front dynamics in a nonlinear singularly perturbed reaction-diffusion problem ⋮ Analysis of an upwind finite-difference scheme for a system of coupled singularly perturbed convection-diffusion equations ⋮ A brief survey on numerical methods for solving singularly perturbed problems ⋮ Special features of strongly coupled systems of convection-diffusion equations with two small parameters ⋮ A posteriori error estimates for one-dimensional convection-diffussion problems ⋮ Lifting solutions of quasilinear convection-dominated problems ⋮ A uniformly convergent nonstandard finite difference scheme for a system of convection-diffusion equations ⋮ Numerical analysis of a strongly coupled system of two singularly perturbed convection-diffusion problems

Cites Work

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• Layer-adapted meshes for convection-diffusion problems
• The Green function and a priori estimates of solutions of monotone three-point singularly perturbed finite-difference schemes
• A parameter robust numerical method for a system of two singularly perturbed convection-diffusion equations
• Maximum Norm A Posteriori Error Estimates for a One-Dimensional Convection-Diffusion Problem
• Analysis of Some Difference Approximations for a Singular Perturbation Problem Without Turning Points
• Sufficient conditions for uniform convergence on layer-adapted grids
• Uniform pointwise convergence of finite difference schemes using grid equidistribution

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