Nonconforming meshes for flow and transport in porous media

In complex systems the domain of calculation for flow and contaminant transport may be the union of several subdomains with very different hydrogeological properties. Because of these differences, the subdomains have different space-time scales. One can think of adjusting the time scales with an almost uniform mesh to obtain a nearly uniform error, but an alternative is to use different space discretizations with a unique time discretization. This implies that the subdomains will have to be discretized independently and consequently the subdomain meshes will not match at the interfaces between subdomains. In order to solve this difficulty mortars and nonmortars techniques were developed. We use here a technique with mortars, that is a technique introducing extra unknowns on the interface between subdomains. This technique is combined with mixed finite elements and the resulting linear system is solved with a domain decomposition method along the lines of [1]. An example from the study of the flow and transport around a deep underground nuclear waste disposal will show the possibilities of the method. [1] G. Pencheva and Y. Yotov, Balancing decomposition for mortar mixed finite element methods, Numerical Algebra With Applications 10 (2003), pp. 159-180.