Space-Time Discontinuous Galerkin Methods for Convection-Diffusion Problems - Application to Wet-Chemical Etching

In this thesis we discuss space-time discontinuous Galerkin (DG) finite element methods for transport phenomena in incompressible flows. The methods, which simultaneously discretize the equations in space and time, provide the necessary flexibility to deal with time deforming meshes and mesh adaptation. In particular, we discuss space-time DG methods for the advection-diffusion equation, which governs the concentration of the acid fluid, and for the incompressible Navier-Stokes equations to model the flow of the acid fluid inside and outside the etching cavity. We provide a detailed theoretical analysis of the stability of the newly developed methods, as well as some simple numerical tests to investigate the accuracy of the methods.