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

Frank F, Knabner P (2017)


Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 2017

Journal

Publisher: EDP SCIENCES S A

Book Volume: 51

Pages Range: 1883-1902

Journal Issue: 5

URI: https://www1.am.uni-erlangen.de/research/publications/Jahr_2017/2017_FrankKn_ConvergenceAnalysisOfBDFDarcyNernstPlanckPoissonSystem

DOI: 10.1051/m2an/2017002

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.

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How to cite

APA:

Frank, F., & Knabner, P. (2017). Convergence analysis of a BDF2/mixed finite element discretization of a Darcy–Nernst–Planck–Poisson system. Mathematical Modelling and Numerical Analysis, 51(5), 1883-1902. https://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." Mathematical Modelling and Numerical Analysis 51.5 (2017): 1883-1902.

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