der Universitat Augsburg

que son tan mios como yo de ustedes Preface The study of complex environmental processes as the transport of contami-nants in water systems is receiving increasing attention due to higher quality standards. The classical approach is the coupled solution of momentum and transport equations. This involves the solution of the ow dynamics, i.e., the determination of the velocity eld, which is used as the convective eld in the transport equation. A problem of signicant relevance in applications is the coupling of surface and subsurface ows. The need for more accurate models and ecient solvers opens a whole research area were Applied Mathematics plays a key role. Water ow above a porous medium is an important but still not solved prob-lem. The diculties stem from several factors: i) The subsurface ow is not well dened as long as no good interface trans-mission conditions are specied. ii) Higher order terms in general Navier/Stokes ows, namely inertial and viscous terms, are not present in the Darcy ow. This thesis attempts to contribute to some insight in this problem by con-sidering coupled Stokes/Darcy ow. It presents a mathematical model for the coupled ow and a nite element approximation. In particular, emphasis is put on the development, analysis, and implementation of ecient solvers based on a heterogeneous domain decomposition methodology. This is a nat-ural and rather exible approach for the solution of problems which involve more than one operator on dierent (disjoint) regions of the domain. A theoretical and experimental analysis is performed. We investigate the dependence of the dierent algorithms with respect to model coecients, domain geometry and boundary conditions, in order to evaluate feasibility and performance of the proposed schemes