A mass-conservative characteristic splitting mixed element method for saltwater intrusion problem

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 L²-norm error estimate is also derived.