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Preprint 13-2014

Numerical solution of singularly perturbed convection-diffusion-reaction problems with two small parameters

Source file is available as :   Portable Document Format (PDF)

Author(s) : Pratibhamoy Das , Volker Mehrmann

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 13-2014

MSC 2000

65L06 Multistep, Runge-Kutta and extrapolation methods
65M12 Stability and convergence of numerical methods

Abstract :
This paper discusses the numerical solution of 1-D convection-diffusion-reaction problems that are singularly perturbed with two small parameters using a new mesh-adaptive upwind scheme that adapts to the boundary layers. The meshes are generated by the equidistribution of a special positive monitor function. Uniform, parameter independent convergence is shown and holds even in the limit that the small parameters are zero. Numerical experiments are presented that illustrate the theoretical findings, and show that the new approach has better accuracy compared with current methods.

Keywords : Parabolic partial differential equation, convection-diffusion-reaction problem, upwind scheme, adaptive mesh, mesh equidistribution, two parameter singular perturbation problem, uniform convergence

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