A MASS‐LUMPING SEMIDISCRETIZATION OF THE SEMICONDUCTOR DEVICE EQUATIONS: Part I: Properties of the semidiscrete problem

The paper deals with a spatial discretization of transient semiconductor device equations. The method can be regarded as a combination of FDM‐ and FEM‐ideas. In the first part of the paper the method is described and—for a weakly acute triangulation—existence, uniqueness, non‐negativity, stability and conservativity of the semidiscrete solution are proved. The second part contains an error estimation under stronger assumptions on the regularity of the analytical solution and on the uniformity of the triangulation respectively. A linear convergence rate is obtained.