学术报告会：Interface-penalty finite elements for interface problems in , H(curl), and H(div)

报告题目：Interface-penalty finite elements for interface problems in , H(curl), and H(div)

报告人：郑伟英(中国科学院数学与系统科学研究院教授、博导)

时间：6月12日15:00-16:00

腾讯会议：会议ID：682 545 606

个人简介：

郑伟英，中国科学院数学与系统科学研究院研究员、科学工程计算国家重点实验室副主任。1996年和1999年于郑州大学分别获学士、硕士学位，2002年于北京大学获博士学位，2006.11—2007.12为慕尼黑工业大学洪堡基金访问学者，2017年获国家杰出青年科学基金资助，2019年任中科院数学与系统科学研究院“冯康首席研究员”。主要从事有限元方法的理论与应用研究，应用领域包括电磁和流体计算等。在大型变压器的可计算建模、分层介质电磁散射以及三维磁流体的高效数值方法等方向取得重要研究成果。

Abstract: Interface-penalty finite element methods are proposed to solve interface problems in , H(curl), H(div) spaces on unfitted tetrahedral meshes. The transmission conditions across the interface are derived in a unified framework for three types of interface problems. Usually, the well-posedness of an H1-elliptic problem requires two transmission conditions for both the solution and the normal flux. However, the well-posedness for H(curl)- or H(div)-elliptic problem requires three transmission conditions. This provides the guideline for designing stable high-order finite element methods on unfitted meshes. Optimal error estimates are proven in energy norms for interface-penalty finite element methods within a unified framework for , H(curl), and H(div). All error estimates are independent of the location of the interface relative to the mesh. Numerical examples show optimal convergence of the proposed finite element methods for piecewise smooth solutions.