A virtual element method for the steady-state Poisson-Nernst-Planck equations on polygonal meshes. (15th November 2021)

• Record Type: Journal Article
• Authors: Liu, Yang; Shu, Shi; Wei, Huayi; Yang, Ying
• Is Part Of: Computers & mathematics with applications. Volume 102(2021)
• Page Start: 95
• Page End: 112
• Publication Date: 2021-11-15
• Subjects: Poisson-Nernst-Planck equations -- Virtual element method -- Error estimate -- Polygonal meshes; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2021.10.002
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: Poisson-Nernst-Planck equations are a nonlinear coupled system which are widely used to describe electrodiffusion processes in biomolecular systems and semiconductors, etc. A virtual element method with order k ( k ≥ 1 ) is proposed to numerically approximate the Poisson-Nernst-Planck equations on polygonal meshes. The error estimates in the H 1 norm are presented for the numerical solution to the Poisson-Nernst-Planck equations. Numerical examples show that the virtual element method can work well on general polygonal elements and the numerical results agree with the theoretical prediction.