On Composite Discontinuous Galerkin Method for simulations of electric   properties of semiconductor devices
  In this paper, a variant of 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 Symmetric Interior Penalty Galerkin (SIPG) method. The proposed method accounts for lower regularity of the solution on the interfaces of devices' layers. It is shown that the discrete problem is well-defined and that discrete solution is unique. Error estimates are derived. Finally, numerical simulations are presented. 
Konrad Sakowski, Leszek Marcinkowski, Pawel Strak, Pawel Kempisty,   Stanislaw Krukowski
math.NA