TU CE GSC CE People at the Graduate School CE Students Robert Schorr Research Project of Robert Schorr

Numerical methods for a parabolic-elliptic interface problem

When working on problems coming from fluid mechanics one has to choose a method that fulfills certain properties to get a stable and physically reliable solution.

In this project, we want to find and analyze a suitable discretization method for a coupled system of partial differential equations (PDEs) consisting of the model problem for transport in porous media, which is a (possibly convection dominated) parabolic time-dependent diffusion-convection-reaction equation on a bounded domain and a diffusion process on the complement of the domain, modeled by the Laplace equation.

To approximate such problems the coupling of a method for the interior problem and the boundary element method (BEM) is of particular interest. Because of the possible convection domination, one would use such methods as an upwind stabilized Finite Volume Method (FVM) or a comparably stabilized Finite Element Method called Streamline Upwind Petrov Galerkin (SUPG).

There are several methods to couple an interior method with BEM, depending on the formulation of the exterior problem and the transmission conditions between the interior and the exterior problem. One such method is the non-symmetric coupling, which has advantages in terms of computational time and has not been analyzed for the time-dependent case, thus it is the main focus of this research project.

Finite Element Method/SUPG, Finite Volume Method, Boundary Element Method, Coupling

Robert Schorr

M.Sc.

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