## Convergent Finite Element Discretizations of the Density Gradient Equation for Quantum Semiconductors

• We study nonlinear finite element discretizations for the density gradient equation in the quantum drift diffusion model. Especially, we give a finite element description of the so--called nonlinear scheme introduced by {it Ancona}. We prove the existence of discrete solutions and provide a consistency and convergence analysis, which yields the optimal order of convergence for both discretizations. The performance of both schemes is compared numerically, especially with respect to the influence of approximate vacuum boundary conditions.

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Author: Rene Pinnau, Jorge Mauricio Ruiz urn:nbn:de:hbz:386-kluedo-14943 Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (270) Preprint English 2007 2007 Technische Universität Kaiserslautern consistency ; convergence ; density gradient equation ; nonlinear finite element method ; numerics Fachbereich Mathematik 510 Mathematik 35J60 Nonlinear elliptic equations 35J70 Degenerate elliptic equations 65N12 Stability and convergence of numerical methods 65N15 Error bounds 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 76Y05 Quantum hydrodynamics and relativistic hydrodynamics [See also 82D50, 83C55, 85A30]

$Rev: 12793$