Drift-Diffusion Systems: Analysis of Discretized Models
A discretization of the steady state drift-diffusion semiconductor model is accurate if for sufficiently small meshwidth h all solutions to the discretized model can be matched in a one to one fashion to solutions to the partial differential equation (pde) system. We employ the convergence of the discretizations of the single pdes in the system (which follows by standard finite element convergence theory) to obtain such a one to one matching. However, the proof requires the introduction of an additional hypothesis of nonsingularity of the system which can only be verified by an analysis of the entire coupled model. Furthermore, the mesh and the discretization procedure must be chosen appropriately so that a priori maximum estimates on the solution for the original system hold for the discretized model as well.
KeywordsDiscretized Model Discretization Error Discretization Procedure Maximum Bound Finite Difference Discretizations
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