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In this paper we introduce a new method for numerically solving the equations of the hydrodynamic model forsemiconductor devices in two space dimensions. The method combines a standard mixed finite element method,used to obtain directly an approximation to the electric field, with the so-called Runge-Kutta DiscontinuousGalerkin (RKDG) method, originally devised for numerically solving multi-dimensional hyperbolic systems ofconservation laws, which is applied here to the convective part of the equations. Numerical simulations showingthe performance of the new method are displayed, and the results compared with those obtained by usingEssentially Nonoscillatory (ENO) finite difference schemes. From the perspective of device modeling, thesemethods are robust, since they are capable of encompassing broad parameter ranges, including those for whichshock formation is possible. The simulations presented here are for Gallium Arsenide at room temperature, butwe have tested them much more generally with considerable success

Mixed-RKDG Finite Element Methods for the 2-D Hydrodynamic Model for Semiconductor Device Simulation