A Combined Discontinuous Galerkin Method for Saltwater Intrusion Problem with Splitting Mixed Procedure (Advances in Applied Mathematics and Mechanics, 2018)
In this paper, a new combined method is presented to simulate saltwaterintrusion problem. A splitting positive definite mixed element method is used to solvethe water head equation, and a symmetric discontinuous Galerkin (DG) finite elementmethod is used to solve the concentration equation. The introduction of these two numericalmethods not only makes the coefficient matrixes symmetric positive definite,but also does well with the discontinuous problem. The convergence of this method isconsidered and the optimal $L^2$-norm error estimate is also derived.