四川师范大学学报（自然科学版）2025，Vol.48Issue(4)：543-550,8.DOI:10.3969/j.issn.1001-8395.2025.04.012
求解Brinkman方程的一种压力鲁棒协调间断有限元法
A Pressure-robust Conforming Discontinuous Galerkin Finite Element Method for the Brinkman Equation
摘要
Abstract
In this paper,a new conforming discontinuous Galerkin finite element method is proposed to solve the Brinkman equa-tion.This method adopts discontinuous finite element space,but its discrete format maintains the concise characteristics of the confor-ming finite element method in form.This method not only uses H(div)finite element space to approximate the velocity space,but also draws on the idea of the weak Galerkin finite element method,that is,the weak gradient operator ▽ w is used instead of the gradient operator ▽ in the variational form.Besides,the gradient operator ▽ is approximated in ▽ wv∈[Pk+1(T)]d ×d space.The new con-forming discontinuous Galerkin finite element method has the following advantages:1)The velocity retains the physical property of the Brinkman equation without divergence.2)The error of the velocity is independent of the error of the pressure.3)There is no need to add complex stabilization terms to enhance the continuity of the velocity in the tangential direction.For the constructed discrete form,its stability and convergence are analyzed in detail,and velocity and pressure under different norms are obtained.The theoretical re-sults are verified by numerical examples.关键词
Brinkman方程/压力鲁棒/H(div)空间/弱梯度算子/协调DGKey words
Brinkman equations/pressure-robust/H(div)space/weak gradient operator/conforming discontinuous Galerkin分类
数理科学引用本文复制引用
陈俊杰,张莉,黄潇莹..求解Brinkman方程的一种压力鲁棒协调间断有限元法[J].四川师范大学学报（自然科学版）,2025,48(4):543-550,8.基金项目
国家自然科学基金(11871138)和四川省科技计划项目(2022JDTD0019) （11871138）
