Work

Analysis of a class of globally divergence-free linearized fully discrete WG methods for unsteady Brinkman-Forchheimer equations

Year: 2025

Type: article

Abstract: In this paper, we develop and analyze a class of linearized fully discrete weak Galerkin (WG) finite element methods for the unsteady Brinkman-Forchheimer model. For spatial discretization, the WG methods utilize the piecewise polynomials of degrees m ( m ≥ 1) and m − 1 to approximate the velocity and the pressure within the interior of elements, respectively. Additionally, piecewise polynomials of degree m are employed for their corresponding numerical traces on the element interfaces. For temporal discretization, a linearized backward Euler difference scheme is formulated, where semi-implicit techniques are adopted to deal with the nonlinear terms. The proposed methods ensure that the velocity approximation is globally divergence - free. The well-posedness and optimal error estimates, both in the energy norm and L 2 norm, are rigorously derived. Numerical tests are conducted to validate the established theoretical results.

Source: Journal of Computational and Applied Mathematics

DOI: 10.1016/j.cam.2025.117278

Authors: Xiaojuan Wang, Xiaoping Xie, Shiquan Zhang

Institutions: Shanxi Agricultural University, Sichuan University

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,250

Funders: National Natural Science Foundation of China, Natural Science Foundation of Sichuan Province