Convergence analysis of a BDF2/mixed finite element discretization of a Darcy–Nernst–Planck–Poisson system

Beitrag in einer Fachzeitschrift
(Originalarbeit)


Details zur Publikation

Autor(en): Frank F, Knabner P
Zeitschrift: Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique Et Analyse Numerique
Verlag: EDP SCIENCES S A
Jahr der Veröffentlichung: 2017
Band: 51
Heftnummer: 5
Seitenbereich: 1883-1902
ISSN: 0764-583X


Abstract

This paper presents an a priori error analysis of a fully discrete scheme for the numerical solution of the transient, nonlinear Darcy-Nernst-Planck-Poisson system. The scheme uses the second order backward difference formula (BDF2) in time and the mixed finite element method with Raviart-Thomas elements in space. In the first step, we show that the solution of the underlying weak continuous problem is also a solution of a third problem for which an existence result is already established. Thereby a stability estimate arises, which provides an L-∞ bound of the concentrations / masses of the system. This bound is used as a level for a cut-off operator that enables a proper formulation of the fully discrete scheme. The error analysis works without semi-discrete intermediate formulations and reveals convergence rates of optimal orders in time and space. Numerical simulations validate the theoretical results for lowest order finite element spaces in two dimensions.


FAU-Autoren / FAU-Herausgeber

Frank, Florian Prof. Dr.
Professur für Angewandte Mathematik (Mathematische Modellierung)
Knabner, Peter Prof. Dr.
Lehrstuhl für Angewandte Mathematik


Zitierweisen

APA:
Frank, F., & Knabner, P. (2017). Convergence analysis of a BDF2/mixed finite element discretization of a Darcy–Nernst–Planck–Poisson system. Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique Et Analyse Numerique, 51(5), 1883-1902. https://dx.doi.org/10.1051/m2an/2017002

MLA:
Frank, Florian, and Peter Knabner. "Convergence analysis of a BDF2/mixed finite element discretization of a Darcy–Nernst–Planck–Poisson system." Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique Et Analyse Numerique 51.5 (2017): 1883-1902.

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Zuletzt aktualisiert 2018-26-11 um 17:08