Practical Application of the Galerkin Finite Element Method with a Mass Conservation Scheme under Dirichlet Boundary Conditions to Solve Groundwater Problems

The Galerkin finite element method (FEM) has long been used to solve groundwater flow equations and compute the mass balance in a region. In this study, we proposed a simple, new computational FEM procedure for global mass balance computations that can simultaneously obtain boundary fluxes at Dirichlet boundary nodes and finite element hydraulic heads at all nodes in only one step, whereas previous approaches usually require two steps. In previous approaches, the first step obtains the Galerkin finite element hydraulic heads at all nodes, and then, the boundary fluxes are calculated using the obtained Galerkin finite element hydraulic heads in a second step. Comparisons between the new approach proposed in this study and previous approaches, such as Yeh’s approach and a conventional differential approach, were performed using two practical groundwater problems to illustrate the improved accuracy and efficiency of the new approach when computing the global mass balance or boundary fluxes. From the results of the numerical experiments, it can be concluded that the new approach provides a more efficient mass balance computation scheme and a much more accurate mass balance computation compared to previous approaches that have been widely used in commercial and public groundwater software.