An Adaptive Grid Method for Singularly Perturbed Time-Dependent Convection-Diffusion Problems. (2nd November 2016)

• Record Type: Journal Article
• Authors: Chen, Yanping; Liu, Li-Bin
• Is Part Of: Communications in computational physics. Volume 20:Number 5(2016:Nov.)
• Page Start: 1340
• Page End: 1358
• Publication Date: 2016-11-02
• Subjects: 65L10, -- 65L12, -- 65L50; Uniform convergence, -- singularly perturbed, -- convection-diffusion problems, -- adaptive grid, -- an upwind finite difference scheme; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.240315.301215a
• Languages: English
• ISSNs: 1815-2406

Abstract

Abstract: In this paper, we study the numerical solution of singularly perturbed time-dependent convection-diffusion problems. To solve these problems, the backward Euler method is first applied to discretize the time derivative on a uniform mesh, and the classical upwind finite difference scheme is used to approximate the spatial derivative on an arbitrary nonuniform grid. Then, in order to obtain an adaptive grid for all temporal levels, we construct a positive monitor function, which is similar to the arc-length monitor function. Furthermore, the ε -uniform convergence of the fully discrete scheme is derived for the numerical solution. Finally, some numerical results are given to support our theoretical results.