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Journal of Scientific Computing

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28-02-2017

Linearized Conservative Finite Element Methods for the Nernst–Planck–Poisson Equations

Authors: Huadong Gao, Dongdong He

Published in: Journal of Scientific Computing | Issue 3/2017

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Abstract

The aim of this paper is to present and study new linearized conservative schemes with finite element approximations for the Nernst–Planck–Poisson equations. For the linearized backward Euler FEM, an optimal \(L^2\) error estimate is provided almost unconditionally (i.e., when the mesh size h and time step \(\tau \) are less than a small constant). Global mass conservation and electric energy decay of the schemes are also proved. Extension to second-order time discretizations is given. Numerical results in both two- and three-dimensional spaces are provided to confirm our theoretical analysis and show the optimal convergence, unconditional stability, global mass conservation and electric energy decay properties of the proposed schemes.

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Title: Linearized Conservative Finite Element Methods for the Nernst–Planck–Poisson Equations
Authors: Huadong Gao
Dongdong He
Publication date: 28-02-2017
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 3/2017
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-017-0400-4

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