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