Higher Order Stabilized Surface Finite Element Methods for Diffusion-Convection-Reaction Equations on Surfaces with and without Boundary

The numerical simulation of free surface and two-phase flows is an area of high interest in fluid dynamics. Thereby, the fluid flow can be influenced by so called surfactants. Surfactant is an abbreviation for surface active agent and names a chemical compound, which can adsorb at the surface and change the surface tension. This influences the fluid motion. To model the influence of surfactants, diusion-convection-reaction equations in the fluid phase, the bulk, and on the surface are required.

In this work the diusion-convection-reaction equation on surfaces with and without boundary is studied. First and higher order approximations of the curved surface are used as finite element meshes. The corresponding operators on the smooth and the discrete surface are introduced. Unique solvability of the weak and the discretized problem are shown and an error analysis for first and higher order finite elements has been taken out.