On a Petrov-Galerkin method for the electrical and thermal behaviour of semiconductor devices in two dimensions (Q1098602)

The author considers the stationary case of the thermal behaviour of semiconductor devices in two dimensions. A non-standard Petrov-Galerkin method is used to obtain a discretization of the weak formulation of the corresponding differential equations - the Poisson equation of elliptic type, the nonlinear Fourier equation, and two continuity equations. The standard finite difference approximations on an arbitrary mesh is obtained for the Poisson and Fourier equations and exponentially fitted finite difference approximations for the two continuity equations. The latter are in fact the usual generalizations to two dimensions of the well-known Scharfetter-Gummel scheme for one-dimensional problems.