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.