Error analysis of finite element method for Poisson–Nernst–Planck equations

Journal Article · Mon Aug 01 00:00:00 EDT 2016 · Journal of Computational and Applied Mathematics

DOI:https://doi.org/10.1016/j.cam.2016.01.028· OSTI ID:1253865

Sun, Yuzhou; Sun, Pengtao; Zheng, Bin; Lin, Guang

A priori error estimates of finite element method for time-dependent Poisson-Nernst-Planck equations are studied in this work. We obtain the optimal error estimates in L∞(H1) and L2(H1) norms, and suboptimal error estimates in L∞(L2) norm, with linear element, and optimal error estimates in L∞(L2) norm with quadratic or higher-order element, for both semi- and fully discrete finite element approximations. Numerical experiments are also given to validate the theoretical results.

• Research Organization: Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
• DOE Contract Number: AC05-76RL01830
• OSTI ID: 1253865
• Report Number(s): PNNL-SA-114192; KJ0401000
• Journal Information: Journal of Computational and Applied Mathematics, Vol. 301; ISSN 0377-0427
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

Poisson-Nernst-Planck equations
a priori error estimates