Convergent discretizations for the Nernst-Planck-Poisson system

DOI10.1007/s00211-008-0194-2zbMath1178.65106OpenAlexW2060224565MaRDI QIDQ1006843

Andreas Prohl, Markus Schmuck

Publication date: 26 March 2009

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-008-0194-2

zbMATH Keywords

convergencenumerical resultsfinite element methoddiscrete maximum principleNernst-Planck-Poisson equations

Mathematics Subject Classification ID

First-order nonlinear hyperbolic equations (35L60) Hyperbolic conservation laws (35L65) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

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Cites Work

• Unnamed Item
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• On the basic equations for carrier transport in semiconductors
• Long time behavior of solutions of Nernst-Planck and Debye-Hückel drift-diffusion systems
• Nonnegativity preserving convergent schemes for the thin film equation
• Finite-element approximation of a nonlinear degenerate parabolic system describing bacterial pattern formation
• Finite element approximation of a nonlinear cross-diffusion population model
• On the time-dependent drift-diffusion model for semiconductors
• Global solutions of the time-dependent drift-diffusion semiconductor equations
• On large time asymptotics for drift-diffusion-poisson systems
• Incompressible Ionized Non-Newtonian Fluid Mixtures
• Convergent finite element discretizations of the Navier-Stokes-Nernst-Planck-Poisson system
• The Stability in L p and W p 1 of the L 2 -Projection onto Finite Element Function Spaces
• A Discretization Scheme for a Quasi-Hydrodynamic Semiconductor Model
• Finite Element Approximation of the Nonstationary Navier–Stokes Problem. I. Regularity of Solutions and Second-Order Error Estimates for Spatial Discretization
• The Debye system: existence and large time behavior of solutions
• Convergence Past Singularities for a Fully Discrete Approximation of Curvature-Driven Interfaces
• On the Discretization of van Roosbroeck's Equations with Magnetic Field
• Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis
• Weakened acute type condition for tetrahedral triangulations and the discrete maximum principle
• ANALYSIS OF THE NAVIER–STOKES–NERNST–PLANCK–POISSON SYSTEM
• Asymptotic behaviour of a finite-volume scheme for the transient drift-diffusion model
• Asymptotic behavior of the drift-diffusion semiconductor equations

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