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A Combined Discontinuous Galerkin Method for Saltwater Intrusion Problem with Splitting Mixed Procedure

Published online by Cambridge University Press:  17 January 2017

Jiansong Zhang*
Affiliation:
Department of Applied Mathematics, China University of Petroleum, 66 Changjiang West Road, Qingdao 266580, China
Jiang Zhu*
Affiliation:
Laboratório Nacional de Computação Científica, MCTI, Avenida Getúlio Vargas 333, 25651-075 Petrópolis, RJ, Brazil
Danping Yang*
Affiliation:
Department of Mathematics, East China Normal University, Shanghai 200062, China
*
*Corresponding author. Email:[email protected] (J. Zhang), [email protected] (J. Zhu), [email protected] (D. Yang)
*Corresponding author. Email:[email protected] (J. Zhang), [email protected] (J. Zhu), [email protected] (D. Yang)
*Corresponding author. Email:[email protected] (J. Zhang), [email protected] (J. Zhu), [email protected] (D. Yang)
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Abstract

In this paper, a new combined method is presented to simulate saltwater intrusion problem. A splitting positive definite mixed element method is used to solve the water head equation, and a symmetric discontinuous Galerkin (DG) finite element method is used to solve the concentration equation. The introduction of these two numerical methods not only makes the coefficient matrixes symmetric positive definite, but also does well with the discontinuous problem. The convergence of this method is considered and the optimal L2-norm error estimate is also derived.

Type
Research Article
Copyright
Copyright © Global-Science Press 2017 

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