A rotated monotone difference scheme for the two-dimensional anisotropic drift-diffusion equation
For the discretization of the steady-state two-dimensional anisotropic drift-diffusion equation a rotated upwind discretization is presented, taking into account the local characteristic nature of the solution. The special feature of the presented algorithm lie in the projection of the governing partial differential equation onto two orthogonal axes, to yield a vanishing mixed derivative term, and in the utilization of the upwind flow of information. The scheme produces an \(M\)-matrix which guarantees an oscillation-free solution and which enables the discrete system to be solved using standard iterative methods. The method is illustrated by numerical examples for which the analytic solutions are known.
scientific article; zbMATH DE number 1212285