Journal
JOURNAL OF SCIENTIFIC COMPUTING
Volume 72, Issue 3, Pages 1269-1289Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-017-0400-4
Keywords
Nernst-Planck-Poisson equations; Finite element methods; Unconditional convergence; Optimal error estimate; Conservative schemes
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Funding
- National Natural Science Foundation of China (NSFC) [11501227, 11402174]
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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 error L-2 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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