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 (permanent link):urn:nbn:de:hbz:386-kluedo-14943
Serie (Series number):Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (270)
Document Type:Preprint
Language of publication:English
Year of Completion:2007
Year of Publication:2007
Publishing Institute:Technische Universität Kaiserslautern
Tag:consistency ; convergence ; density gradient equation ; nonlinear finite element method ; numerics
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:510 Mathematik
MSC-Classification (mathematics):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]

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