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

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  17 January 2017

Jiansong Zhang ,
Jiang Zhu  and
Danping Yang
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:jszhang@upc.edu.cn (J. Zhang), jiang@lncc.br (J. Zhu), dpyang@math.ecnu.edu.cn (D. Yang)
*Corresponding author. Email:jszhang@upc.edu.cn (J. Zhang), jiang@lncc.br (J. Zhu), dpyang@math.ecnu.edu.cn (D. Yang)
*Corresponding author. Email:jszhang@upc.edu.cn (J. Zhang), jiang@lncc.br (J. Zhu), dpyang@math.ecnu.edu.cn (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.

Keywords

Splitting mixed systemdiscontinuous Galerkin methodsaltwater intrusion problemconvergence analysis

MSC classification

Secondary: 65M12: Stability and convergence of numerical methods 65M15: Error bounds 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 3 , June 2017 , pp. 651 - 666
Copyright
Copyright © Global-Science Press 2017 

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