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 of Scientific Computing – Springer Journals
Published: Feb 28, 2017
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