Existence of bounded discrete steady state solutions of the van Roosbroeck system on boundary conforming Delaunay grids

The paper summarizes properties of Delaunay grids, Voronoi diagrams and presents a weak formulation of the Scharfetter-Gummel-scheme on d dimensional simplex grids. Other technical details, like the weak discrete maximum principle, are introduced, too. The advantage of the formalism is a direct ´reuse´ of analytic results to obtain the discrete estimates. The results of (Zlamal, 1984) (restricted to the non obtuse angle case) can be extended in more detail to relevant 3d situations.