A mass-conservative characteristic splitting mixed element method for saltwater intrusion problem
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Authors
Jiansong Zhang
- Department of Applied Mathematics, China University of Petroleum, Qingdao 266580, China.
Yuezhi Zhang
- Department of Applied Mathematics, China University of Petroleum, Qingdao 266580, China.
Zhaohui Liu
- Department of Applied Mathematics, China University of Petroleum, Qingdao 266580, China.
Abstract
A new characteristic mixed finite element method is developed for solving saltwater intrusion problem. In this algorithm, the splitting mixed finite element (SMFE) method is applied for solving the parabolic-type water head equation, and the mass-conservative characteristic (MCC) finite element method is applied for solving the convection-diffusion type concentration equation. The application of the splitting mixed element method results in a symmetric positive definite coefficient matrix of the mixed element system and separating the flux equation from the water head equation. While the mass-conservative characteristic finite element method does well in handling convection-dominant diffusion problem and keeps mass balance. The convergence of this method is considered and the optimal \(L^2\)-norm error estimate is also derived.
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ISRP Style
Jiansong Zhang, Yuezhi Zhang, Zhaohui Liu, A mass-conservative characteristic splitting mixed element method for saltwater intrusion problem, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 11, 6102--6118
AMA Style
Zhang Jiansong, Zhang Yuezhi, Liu Zhaohui, A mass-conservative characteristic splitting mixed element method for saltwater intrusion problem. J. Nonlinear Sci. Appl. (2017); 10(11):6102--6118
Chicago/Turabian Style
Zhang, Jiansong, Zhang, Yuezhi, Liu, Zhaohui. "A mass-conservative characteristic splitting mixed element method for saltwater intrusion problem." Journal of Nonlinear Sciences and Applications, 10, no. 11 (2017): 6102--6118
Keywords
- Method of characteristics
- mass-conservative
- splitting mixed finite element
- error estimate
- saltwater intrusion problem
MSC
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