A DISCRETIZATION SCHEME FOR A QUASI-HYDRODYNAMIC SEMICONDUCTOR MODEL

A discretization scheme based on exponential fitting mixed finite elem ents is developed for the quasi-hydrodynamic (or nonlinear drift-diffu sion) model for semiconductors. The diffusion terms are nonlinear and of degenerate type. The presented two-dimensional scheme maintains the good features already shown by the mixed finite elements methods in t he discretization of the standard isothermal drift-diffusion equations (mainly, current conservation and good approximation of sharp shapes) . Moreover, it deals with the possible formation of vacuum sets. Sever al numerical tests show the robustness of the method and illustrate th e most important novelties of the model.