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Volume 9, Issue 3
A Combined Discontinuous Galerkin Method for Saltwater Intrusion Problem with Splitting Mixed Procedure

Jiansong Zhang, Jiang Zhu & Danping Yang

DOI: 10.4208/aamm.2015.m1026

Adv. Appl. Math. Mech., 9 (2017), pp. 651-666.

Published online: 2018-05

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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 $L^2$-norm error estimate is also derived.

  • Keywords

Splitting mixed system, discontinuous Galerkin method, saltwater intrusion problem, convergence analysis.

  • AMS Subject Headings

65M12, 65M15, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-9-651, author = {Zhang , JiansongZhu , Jiang and Yang , Danping}, title = {A Combined Discontinuous Galerkin Method for Saltwater Intrusion Problem with Splitting Mixed Procedure}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {9}, number = {3}, pages = {651--666}, 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 $L^2$-norm error estimate is also derived.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2015.m1026}, url = {http://global-sci.org/intro/article_detail/aamm/12168.html} }
TY - JOUR T1 - A Combined Discontinuous Galerkin Method for Saltwater Intrusion Problem with Splitting Mixed Procedure AU - Zhang , Jiansong AU - Zhu , Jiang AU - Yang , Danping JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 651 EP - 666 PY - 2018 DA - 2018/05 SN - 9 DO - http://doi.org/10.4208/aamm.2015.m1026 UR - https://global-sci.org/intro/article_detail/aamm/12168.html KW - Splitting mixed system, discontinuous Galerkin method, saltwater intrusion problem, convergence analysis. AB -

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 $L^2$-norm error estimate is also derived.

Zhang , JiansongZhu , Jiang and Yang , Danping. (2018). A Combined Discontinuous Galerkin Method for Saltwater Intrusion Problem with Splitting Mixed Procedure. Advances in Applied Mathematics and Mechanics. 9 (3). 651-666. doi:10.4208/aamm.2015.m1026
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