BIMSA > BIMSA Computational Math Seminar BIMSA Computational Math Seminar Nonconforming finite element exterior calculus and primal schemes for the Hodge Laplace equation
Nonconforming finite element exterior calculus and primal schemes for the Hodge Laplace equation
Organizers
Tahereh Eftekhari , Pipi Hu , Xin Liang , Zhiting Ma , Hamid Mofidi , Chunmei Su , Axel G.R. Turnquist , Li Wang , Fansheng Xiong , Shuo Yang , Wuyue Yang
Speaker
Shuo Zhang
Time
Wednesday, May 27, 2026 2:00 PM - 3:00 PM
Venue
A3-4-312
Online
Zoom 518 868 7656 (BIMSA)
Abstract
The theory of conforming finite element exterior calculus has been well developed, and the research has now reached a point where extension is appropriate to nonconforming methods, of which some progress will be reported. This talk will firstly present a unified family of consistent nonconforming finite element spaces for $H\Lambda^k$ in $\mathbb{R}^n$, $n\geqslant 1$, $0\leqslant k\leqslant n$. The spaces employ piecewise Whitney forms as shape functions, based on which discrete de Rham complexes with commutative diagrams are established. A theory of nonconforming finite element exterior calculus is then given. Its combination with the classical conforming one helps reconstructed some structural properties at discrete level, which can not be done by the conforming FEEC alone. Finally, based on these new spaces and the new construction approach, new primal schemes are introduced for the Hodge Laplace problem, for which reasonable conforming primal discretizations are impossible to construct.
Speaker Intro
张硕，中国科学院数学与系统科学研究院副研究员。主要从事偏微分方程数值算法研究，研究兴趣包括有限元方法、神经网络方法等。以第一作者或通讯作者在Numer. Math.，SIAM J Numer Anal.，J Comput. Physics等刊物和AAAI等会议发表论文多篇。曾获中国计算数学学会优秀青年论文奖二等奖及一等奖各一项。受邀在国际基础科学大会和世界华人数学家大会做邀请报告。是中国计算机学会高级会员，CSIAM第一届金融科技与算法专业委员会委员，和CSIAM信息和通讯技术领域的数学专委会委员。