In this paper, a variant of the discretization of the van Roosbroeck equations in the equilibrium state with the composite discontinuous Galerkin method for the rectangular domain is discussed. It is based on the symmetric interior penalty Galerkin (SIPG) method. The proposed method accounts for lower regularity of the solution at the interfaces of the layers of the device. It is shown that the discrete problem is well defined and that the discrete solution is unique. Error estimates are derived. Finally, numerical simulations are presented.
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