论文丨Xiaojuan Wang, Jihong Xiao, Xiaoping Xie and Shiquan Zhang：Robust globally divergence-free weak Galerkin methods for unsteady incompressible convective Brinkman–Forchheimer equations

本文（Robust globally divergence-free weak Galerkin methods for unsteady incompressible convective Brinkman–Forchheimer equations）原载Communications in Nonlinear Science and Numerical Simulation，由四川大学张世全副教授等科研人员创作，系四川大学智慧法治超前部署学科系列学术成果。后续会持续分享四川大学智慧法治超前部署学科系列学术成果，欢迎大家阅读。

Abstract:This paper develops and analyzes a class of semi-discrete and fully discrete weak Galerkin finite element methods for unsteady incompressible convective Brinkman-Forchheimer equations. For the spatial discretization, the methods adopt the piecewise polynomials of degrees m\ (m\geq1) and m-1 respectively to approximate the velocity and pressure inside the elements, and piecewise polynomials of degree m to approximate their numerical traces on the interfaces of elements. In the fully discrete method, the backward Euler difference scheme is used to approximate the time derivative. The methods are shown to yield globally divergence-free velocity approximation. Optimal a priori error estimates in the energy norm and L^2 norm are established. A convergent linearized iterative algorithm is designed for solving the fully discrete system. Numerical experiments are provided to verify the theoretical results.

Xiaojuan Wang, Jihong Xiao, Xiaoping Xie and Shiquan Zhang. Robust globally divergence-free weak Galerkin methods for unsteady incompressible convective Brinkman–Forchheimer equations. Communications in Nonlinear Science and Numerical Simulation. Volume 143, April 2025, 108578.（论文下载）