Combining Finite element methods and level set formulation for the simulation of ground water- surface water systems.

The goal of this project is to develop and analyze stabilized finite element methods for the simulation of coupled ground water - surface water systems. These problems are modeled by DarcyStokes systems coupled through interface boundary conditions. A unified finite element stabilization approach, for the simulation of coupled ground water - surface water systems, is investigated. The success of symmetric stabilization such as local projection and sub-grid methods; inherited from solving steady state Stokes like problems is extended to the coupling of ground water ? surface water flow problems. Existence and uniqueness results of a weak solution and numerical scheme are investigated. In this work, we intend to derive priori error estimates for the numerical scheme and use a level set method to track the interface between the two separate flow domains. In addition, we will use advantageous non-iterative portioned methods approach which allows uncoupling into one Stokes and one Darcy problems per time step. Another way that we will consider, in project, for uncoupling ground water ? surface water systems is the use of splitting schemes.