报告题目：Weak Galerkin finite element method for interface problems with curved interface

报告人：杨琳 中国科学院数学与系统科学研究院

报告时间：2025年11月16日 下午15:00-16:00

报告地点：#腾讯会议：544-638-730

校内联系人：张剑桥 [email protected]

报告摘要：In this work, we use the weak Galerkin (WG) finite element method to solve interface problems with curved interface. When solving such problems on fitted meshes, the geometric error introduced by approximating the curved interface with straight segments limits the accuracy of high-order numerical methods. To overcome this challenge, we directly construct the WG space on curved interface elements, thus avoiding geometric error. To demonstrate the effectiveness of this method, we apply it to the Stokes interface problem as an example. However, this method may become inefficient for problems with moving interfaces, as the meshes must be updated to capture the evolving interface. Therefore, we consider solving interface problems on unfitted meshes. In our method, standard finite element spaces are used in non-interface elements, while immersed weak function spaces that exactly satisfy interface conditions are employed in the interface elements. The immersed interface function space is constructed to maintain optimal approximation properties. At the same time, the proposed numerical scheme achieves optimal convergence rates. We demonstrate the effectiveness of the scheme using a second-order elliptic interface problem as an example.

报告人简介：杨琳，2025年于吉林大学获得博士学位，目前为中国科学院数学与系统科学研究院博士后，主要研究方向为非标准有限元方法、界面问题的非拟合网格数值方法等。