A finite-volume scheme for the multidimensional quantum drift-diffusion model for semiconductors

DOI10.1002/NUM.20592zbMath1251.82055OpenAlexW2118846346MaRDI QIDQ3097949

Claire Chainais-Hillairet, Marguerite Gisclon, Ansgar Jüngel

Publication date: 10 November 2011

Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/num.20592

zbMATH Keywords

existence of solutionsnumerical convergencefinite-volume methoddiscrete Sobolev inequalityquantum Bohm potentialquantum semiconductor devicesdensity-gradient model

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Second-order elliptic equations (35J15) Statistical mechanics of semiconductors (82D37) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Higher-order elliptic equations (35J30) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (4)

Mathematical modeling of a discontinuous solution of the generalized Poisson-Nernst-Planck problem in a two-phase medium ⋮ On generalized Poisson-Nernst-Planck equations with inhomogeneous boundary conditions: a-priori estimates and stability ⋮ Entropy-stable and entropy-dissipative approximations of a fourth-order quantum diffusion equation ⋮ On gradient structures for Markov chains and the passage to Wasserstein gradient flows

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