Nonconforming finite elements satisfying a strong discrete Mirande-Talenti inequality
报告题目 :Nonconforming finite elements satisfying a strong discrete Mirande-Talenti inequality
报告专家:田舒丹(德国耶拿大学)
报告时间：2022年12月20日下午14：30-15：30
报告地点：腾讯会议：322-144-514 无密码
报告摘要：
In this talk, I will introduce two families of new $H^2$-nonconforming elements in 2D and 3D, which satisfy a strong discrete Mirande-Talenti inequality. Our construction based on $C^0$ elements with $C^1$ continuity on the vertices (2D) or edges (3D), such as the Hermite element. One directly application of those two families elements is to solve non-divergence form equations, which can avoid use additional stabilization terms. For this reason, the Cea estimation and the posterior error estimator can be obtained naturally. Solving biharmonic equations is another good application. Compared with traditional high order $H^2$-nonconforming elements, our elements have less degrees of freedom. Finally， some numerical results are provided to illustrate the performance of the new methods。
报告专家：
田舒丹，2021年博士毕业于北京大学数学科学学院，师从胡俊教授。2021年至今在德国耶拿大学跟随Dietmar Gallistal教授做博士后，其主要研究方向为有限元方法，具体研究兴趣包括弹性力学的有限元方法、四阶椭圆问题的非协调元设计以及非散度型方程的数值求解。目前在SIAM系列期刊、Comput. Math. & Appl、中国科学数学等期刊上发表多篇学术论文。
邀请人：杨凡意