"Stabilizer-free Weak Galerkin Method and its Optimal L² Error Estimate" by Wenjuan Li, Fuzheng Gao et al.
 

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.

Department(s)

Mathematics and Statistics

Comments

National Natural Science Foundation of China, Grant 11871038

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

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