Uniform convergence analysis of finite difference approximations for advection–reaction–diffusion problem on adaptive grids

DOI10.1080/00207160.2011.591928zbMath1244.65115OpenAlexW2023843476WikidataQ57644444 ScholiaQ57644444MaRDI QIDQ2885550

Yu-Jiang Wu, Linan Sun, Ai-Li Yang

Publication date: 23 May 2012

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160.2011.591928

zbMATH Keywords

stabilitymaximum principleconvergencesingular perturbationfinite difference methodnumerical exampleserror estimationboundary layeradaptive meshmesh equidistributionadvection-reaction-diffusion problem

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) 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) Singular perturbations for ordinary differential equations (34E15) Finite difference and finite volume methods for ordinary differential equations (65L12) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50) Numerical solution of singularly perturbed problems involving ordinary differential equations (65L11)

Related Items (2)

A posteriori error analysis for a fractional differential equation ⋮ Dissipativity ofθ-methods for a class of advection–reaction–diffusion equations with both fixed and distributed delays

Cites Work

• Unnamed Item
• Unnamed Item
• The fluid dynamic approach to equidistribution methods for grid adaptation
• On the numerical solutions of two-point singularly perturbed boundary value problems
• An almost third order finite difference scheme for singularly perturbed reaction-diffusion systems
• Analysis of difference approximations to a singularly perturbed two-point boundary value problem on an adaptively generated grid
• Uniform pointwise convergence for a singularly perturbed problem using arc-length equidistribution.
• Convergence analysis of finite difference approximations on equidistributed grids to a singularly perturbed boundary value problem
• Numerical solution of a singularly perturbed two-point boundary value problem using equidistribution: Analysis of convergence
• An adaptive mesh redistribution method for the incompressible mixture flows using phase-field model
• Uniform convergence analysis of finite difference approximations for singular perturbation problems on an adapted grid
• Maximum Norm A Posteriori Error Estimates for a One-Dimensional Convection-Diffusion Problem
• Uniform convergence analysis of an upwind finite-difference approximation of a convection-diffusion boundary value problem on an adaptive grid
• A Robust Adaptive Method for a Quasi-Linear One-Dimensional Convection-Diffusion Problem
• An analysis of stability and convergence of a finite-difference discretization of a model parabolic PDE in 1D using a moving mesh
• Uniform pointwise convergence of finite difference schemes using grid equidistribution
• Moving mesh methods in multiple dimensions based on harmonic maps

This page was built for publication: Uniform convergence analysis of finite difference approximations for advection–reaction–diffusion problem on adaptive grids