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
-norm error estimate is also derived.