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

Linearized Conservative Finite Element Methods for the Nernst–Planck–Poisson Equations 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 $$L^2$$ L 2 error estimate is provided almost unconditionally (i.e., when the mesh size h and time step $$\tau$$ τ 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Scientific Computing Springer Journals

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

, Volume 72 (3) – Feb 28, 2017
21 pages

/lp/springer_journal/linearized-conservative-finite-element-methods-for-the-nernst-planck-c9hunvvD43
Publisher
Springer Journals
Subject
Mathematics; Algorithms; Computational Mathematics and Numerical Analysis; Mathematical and Computational Engineering; Theoretical, Mathematical and Computational Physics
ISSN
0885-7474
eISSN
1573-7691
D.O.I.
10.1007/s10915-017-0400-4
Publisher site
See Article on Publisher Site

### 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 $$L^2$$ L 2 error estimate is provided almost unconditionally (i.e., when the mesh size h and time step $$\tau$$ τ 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.

### Journal

Journal of Scientific ComputingSpringer Journals

Published: Feb 28, 2017

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