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Main Title: Numerical solution of singularly perturbed convection-diffusion-reaction problems with two small parameters
Author(s): Das, Pratibhamoy
Mehrmann, Volker
Type: Research Paper
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.
Subject(s): parabolic partial differential equation
convection-diffusion-reaction problem
upwind scheme
adaptive mesh
mesh equidistribution
two parameter singular perturbation problem
uniform convergence
Issue Date: 5-Aug-2014
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 65L06 Multistep, Runge-Kutta and extrapolation methods
65M12 Stability and convergence of numerical methods
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2014, 13
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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