报告题目： Analysis and Elimination of Numerical Pressure Dependency in Coupled Stokes-Darcy Problem

报 告 人： 张佳川 副教授 南京工业大学数学系  

报告时间：2025年6月28日上午9:00-10:00

报告地点：腾讯会议：695883840

校内联系人： 卜柯文 [email protected]

报告摘要：This talk presents a pressure-robust mixed finite element method (FEM) for the coupled Stokes-Darcy system. We revisits the rigorous theoretical framework of Layton et al. [2002], where velocity and pressure errors are coupled, masking pressure’s influence on velocity accuracy. To investigate the pressure dependency, we introduce a auxiliary velocity projection that preserves discrete divergence and interface continuity constraints. By analyzing the difference between the discrete and projected velocities, we rigorously prove that classical FEM incurs pressure-dependent consistency errors due to inexact divergence enforcement and approximate interface conditions. To eliminate these errors, we design a pressure-robust method using divergence-free reconstruction operator, which enforce exact divergence constraint and interface continuity. Numerical examples confirm the theory: under high-pressure or low-viscosity, the proposed method reduces velocity errors by orders of magnitude compared to classical method.

报告人简介：张佳川，博士，南京工业大学数学系副教授，研究方向主要为偏微分方程数值解，在SIAM J. Appl. Math.、Commun. Comput. Phy.、J. Sci. Comput.、Numer. Meth. Part. D. E.等杂志发表学术论文十余篇，其研究获得国家自然科学基金、江苏省自然科学基金、江苏省高等学校自然科学基金、南京工业大学科研启动基金支持。