Error analysis of mixed finite element method for Poisson‐Nernst‐Planck system |
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| Authors: | Mingyan He Pengtao Sun |
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| Institution: | 1. The School of Science, Hangzhou Dianzi University, Hangzhou, Zhejiang, People's Republic of China;2. Department of Mathematical Sciences, University of Nevada Las Vegas, Maryland Parkway, Las Vegas, Nevada |
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| Abstract: | To improve the convergence rate in L2 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  norm for the electrostatic potential, and in  and  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 |
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| Keywords: | Poisson‐Nernst‐Planck system mixed finite element method Taylor‐Hood element semidiscretization full discretization the optimal error estimate |
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norm for the electrostatic potential, and in 
and 
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