TY - JOUR ID - TI - The Convergent and Discrete Maximum Principle of Finite Element Methods for solving the Convection-Diffusion-Reaction problem AU - Hashim A.Kashkool AU - suhad J. Khalifa PY - 2012 VL - 11 IS - 20 SP - 19 EP - 30 JO - Misan Journal of Academic Studies مجلة ميسان للدراسات الاكاديمية SN - 1994697X 2706722X AB - 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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