Stabilizer-free Weak Galerkin Method and its Optimal L² Error Estimates for the Time-dependent Poisson—Nernst–Planck Problem
Abstract
This paper concerns a backward Euler stabilizer-free weak Galerkin finite element method (SFWG-FEM) for the time-dependent Poisson–Nernst–Planck (TD-PNP) problem. The scheme we propose utilizes spaces Pk(K), Pk(e), [Pj(K)]2 to approximate the interior, edge, and discrete weak gradient spaces on each element K and edge e⊂∂K, respectively. The proposed method is in a simple format similar to the regular finite element method, compatible with polygonal meshes, flexible in approximation function space, and unconditionally stable in time. Based on a rigorous analysis of a weak Galerkin Ritz projection error, which is derived by a dual problem, the superconvergence of the Ritz projection error estimates in energy norm results in optimal L2 error estimates. Several numerical experiments are conducted to demonstrate our theoretical findings, where Oseen iteration is utilized for the nonlinear coupling terms.
Recommended Citation
W. Li et al., "Stabilizer-free Weak Galerkin Method and its Optimal L² Error Estimates for the Time-dependent Poisson—Nernst–Planck Problem," Communications in Nonlinear Science and Numerical Simulation, vol. 141, article no. 108449, Elsevier, Feb 2025.
The definitive version is available at https://doi.org/10.1016/j.cnsns.2024.108449
Department(s)
Mathematics and Statistics
Keywords and Phrases
Optimal error estimates; Poisson–Nernst–Planck problem; Stabilizer-free weak Galerkin finite element method
International Standard Serial Number (ISSN)
1007-5704
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2025 Elsevier, All rights reserved.
Publication Date
01 Feb 2025
Comments
National Natural Science Foundation of China, Grant 11871038