Error analysis of mixed finite element method for Poisson‐Nernst‐Planck system. Issue 6 (19th June 2017)

• Record Type: Journal Article
• Authors: He, Mingyan; Sun, Pengtao
• Is Part Of: Numerical methods for partial differential equations. Volume 33:Issue 6(2017:Nov.)
• Page Start: 1924
• Page End: 1948
• Publication Date: 2017-06-19
• Subjects: Poisson‐Nernst‐Planck system -- mixed finite element method -- Taylor‐Hood element -- semidiscretization -- full discretization -- the optimal error estimate; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22170
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract : To improve the convergence rate in L 2 norm from suboptimal to optimal for both electrostatic potential and ionic concentrations in Poisson‐Nernst‐Planck (PNP) system, we propose the mixed finite element method in this article to discretize the electrostatic potential equation, and still use the standard finite element method to discretize the time‐dependent ionic concentrations equations. Optimal error estimates in L ∞ ( [ 0, T ] ; L 2 ) norm for the electrostatic potential, and in L ∞ ( [ 0, T ] ; L 2 ) and L ∞ ( [ 0, T ] ; H 1 ) norms for the ionic concentrations are attained. As a by‐product, the electric field can also achieve a higher approximation order in contrast with the standard finite element method for PNP system. Numerical experiments are performed to validate the theoretical results.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1924–1948, 2017