Parallel characteristic mixed element method for saltwater intrusion problem

Numerical simulation of saltwater intrusion problem has attracted more and more attention in the past decades. Based on parallel subspace correction method proposed by Xu (1992), a new overlapping domain decomposition parallel algorithm is constructed to solve saltwater intrusion problem. In this algorithm, the splitting positive definite mixed element method is used to discrete head water equation, while the characteristic Galerkin finite element method is used to approximate concentration equation. The relation between the convergence rate and discretization parameters, including the overlapping degree of the subspaces, is considered. Furthermore, the convergence of this algorithm is analyzed and the corresponding error estimate is given. The convergence result suggests that only two iterations are needed to reach the given accuracy at each time level.