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Superconvergence analysis of finite element method for Poisson–Nernst–Planck equations
Author(s) -
Shi Dongyang,
Yang Huaijun
Publication year - 2019
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22346
Subject(s) - superconvergence , mathematics , finite element method , bilinear interpolation , norm (philosophy) , poisson distribution , nernst equation , interpolation (computer graphics) , nonlinear system , mathematical analysis , poisson's equation , backward euler method , euler equations , physics , classical mechanics , motion (physics) , statistics , electrode , quantum mechanics , political science , law , thermodynamics
This article concerns with the superconvergence analysis of bilinear finite element method (FEM) for nonlinear Poisson–Nernst–Planck (PNP) equations. By employing high accuracy integral identities together with mean value technique, the superclose estimates in H 1 ‐norm are derived for the semi‐discrete and the backward Euler fully‐discrete schemes, which improve the suboptimal error estimate in L 2 ‐norm in the previous literature. Furthermore, the global superconvergence results in H 1 ‐norm are obtained through interpolation postprocessing approach. Finally, a numerical example is provided to confirm the theoretical analysis.