报告题目： 多边形网格上的 Raviart-Thomas 交错间断伽辽金方法
Title: Raviart-Thomas Staggered DG methods on polygonal meshes
报告人 (Speaker)：Eun-Jae Park教授（Yonsei University）
报告时间 (Time)：2025年12月23日(周二) 13：10
报告地点 (Place)： 乐乎新楼 上善厅
邀请人(Inviter)：刘东杰
报告摘要：In this talk, we present a new family of polygonal SDG methods utilizing Raviart-Thomas mixed finite element spaces. Formulated in a mixed setting, the method approximates the primal and dual variables using a locally $H^1$-conforming finite element space and a locally $\vH(\div)$-conforming Raviart--Thomas finite element space, respectively. Unlike in classical mixed FEM, the standard $RT_k \times P_k$ pair is not inf–sup stable in the SDG framework due to the staggered primal–dual mesh structure. To restore stability, the primal space is enriched with bubble type functions on dual elements. The inf-sup stability and optimal convergence are proved. Next, with a simple modification of the loading term we are able to obtain globally $\vH(\div)$-conforming velocity fields. The theoretical results are verified by numerical experiments. Some recent work on the eigenvalue problem will be discussed.