New characteristic difference method with adaptive mesh for one-dimensional unsteady convection-dominated diffusion equations

DOI10.1080/00207160412331291143zbMath1119.65377OpenAlexW2079435989MaRDI QIDQ5699922

Tongke Wang

Publication date: 27 October 2005

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

Full work available at URL: https://doi.org/10.1080/00207160412331291143

zbMATH Keywords

numerical examplesmaximum norm error estimateadaptive mesh methodnew characteristic difference schemeone-dimensional unsteady convection-dominated diffusion equation

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs (65M25) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Initial value problems for second-order parabolic equations (35K15) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

Related Items

A backward approach to certain class of transport equations in any dimension based on the Shannon sampling theorem, Fast successive permutation iterative algorithms for solving convection diffusion equation, Numerical solution of nonlinear advection diffusion reaction equation using high-order compact difference method, Explicit finite difference schemes adapted to advection–reaction equations

Cites Work

• Analysis of difference approximations to a singularly perturbed two-point boundary value problem on an adaptively generated grid
• A second order characteristic finite element scheme for convection-diffusion problems
• The modified method of characteristics with adjusted advection
• On the transport-diffusion algorithm and its applications to the Navier-Stokes equations
• Adaptive defect correction methods for convection dominated, convection diffusion problems
• A priori meshes for singularly perturbed quasilinear two-point boundary value problems
• Finite Difference Methods for Two-Phase Incompressible Flow in Porous Media
• Uniformly High-Order Accurate Nonoscillatory Schemes. I
• Numerical Methods for Convection-Dominated Diffusion Problems Based on Combining the Method of Characteristics with Finite Element or Finite Difference Procedures
• Accurate Monotone Cubic Interpolation
• Moving Mesh Partial Differential Equations (MMPDES) Based on the Equidistribution Principle
• An Optimal-Order Error Estimate for an ELLAM Scheme for Two-Dimensional Linear Advection-Diffusion Equations
• Adaptive Lagrange–Galerkin methods for unsteady convection-diffusion problems
• A high-order Godunov method for one-dimensional convection-diffusion-reaction problems
• A Robust Adaptive Method for a Quasi-Linear One-Dimensional Convection-Diffusion Problem