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The Convergent and Discrete Maximum Principle of Finite Element Methods for solving the Convection-Diffusion-Reaction problem

Authors: Hashim A.Kashkool --- suhad J. Khalifa
Journal: Misan Journal of Acodemic Studies مجلة ميسان للدراسات الاكاديمية ISSN: 1994697X Year: 2012 Volume: 11 Issue: 20 Pages: 19-30
Publisher: Misan University جامعة ميسان

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Abstract

In this paper, we describe several finite element methods for solving theConvection-Diffusion-Reaction problem(CDR)and study two important propertiesfor the approximate solution, the convergent and the discrete maximum principle.For convergence we considered two cases, semi-discrete and discretemethods, for semi-discrete, we prove that all scheme are converge with ) ( r h O ,where h refers to the discretization parameter, 1 1    s r and s is a degree ofpolynomials of finite element space and for discrete we proved that all schemesconverge with ) (   r h O . Finally, the discrete maximum principle and  L - stableare proved.

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The Convergent

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