报告题目：Brinkman问题的压力鲁棒虚单元方法

报告摘要：This talk investigates both a priori and a posteriori error estimates for a pressure-robust and divergence-free virtual element method to approximate the incompressible Brinkman problem on polygonal meshes. The exactly divergence-free property of virtual space preserves the mass-conservation of the system. By extending the lowest-order Raviart–Thomas element to polygonal meshes, we construct a divergence-preserving reconstructor for the discretization of the right-hand side. A rigorous a priori error analysis is developed, showing that the velocity error is independent of both the continuous pressure and the viscosity. Taking advantage of the virtual element method’s ability to handle more general polygonal meshes, we design an adaptive mesh refinement approach and construct a residual-type a posteriori error indicator. This indicator is proven to provide global upper and local lower bounds for the discretization error. Finally, some numerical experiments demonstrate the robustness, accuracy, reliability and efficiency of the method.

报告人简介：陈艳萍，南京邮电大学博士生导师、国务院政府特殊津贴专家（2004）、入选首批教育部新世纪人才计划（2004）、广东省珠江学者特聘教授（2008）。主持获得教育部自然科学二等奖（2017）和广东省科学技术二等奖（2012）；参与获得第二届全国教材建设奖（高等教育类）二等奖（2025）、国家教学成果二等奖（2014）和教育部自然科学一等奖（2011）等。2014-2025年连续 12 年入选 Elsevier 中国高被引学者榜单、2025年入选全球前 2% 顶尖科学家榜单、2023年入选全球顶尖前 10 万科学家排名和数学类全球前 2% 顶尖科学家榜单。主持国家自然科学基金重点项目 1 项、重大研究计划培育项目 1 项、面上项目 8 项。

报告时间：2026年6月18日17:00-18:30

报告地点：武之楼322会议室