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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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Metadaten
Author:Rene Pinnau, Jorge Mauricio Ruiz
URN:urn:nbn:de:hbz:386-kluedo-14943
Series (Serial Number):Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (270)
Document Type:Preprint
Language of publication:English
Year of Completion:2007
Year of first Publication:2007
Publishing Institution:Technische Universität Kaiserslautern
Date of the Publication (Server):2007/05/11
Tag:consistency; convergence; density gradient equation; nonlinear finite element method; numerics
Faculties / Organisational entities:Kaiserslautern - Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Jxx Elliptic equations and systems [See also 58J10, 58J20] / 35J60 Nonlinear elliptic equations
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Jxx Elliptic equations and systems [See also 58J10, 58J20] / 35J70 Degenerate elliptic equations
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N12 Stability and convergence of numerical methods
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N15 Error bounds
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
76-XX FLUID MECHANICS (For general continuum mechanics, see 74Axx, or other parts of 74-XX) / 76Yxx Quantum hydrodynamics and relativistic hydrodynamics [See also 82D50, 83C55, 85A30] / 76Y05 Quantum hydrodynamics and relativistic hydrodynamics [See also 82D50, 83C55, 85A30]
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011