報告題目：Finite element diagram chasing
報 告 人：Kaibo Hu 胡凱博 博士 University of Minnesota
報告時間：2020年8月26日10:00-11:00
報告地點：騰訊會議 ID：418 227 590
https://meeting.tencent.com/s/4M7QFoY5DCgN
校内聯系人：王翔 wxjldx@jlu.edu.cn
報告摘要：
There is a close relation between Maxwell’s equations and the de Rham complex. The perspective of continuous and discrete differential forms has inspired key progress in computational electromagnetism. This complex point of view also plays an important role in, e.g., continuum theory of defects, intrinsic elasticity and relativity.
In this talk, we briefly review the de Rham complexes and their smoother versions, known as the Stokes complexes with applications in fluid mechanics. Then we generate new complexes from them and study their algebraic and analytic properties. As an example, we construct Sobolev and finite element elasticity complexes by diagram chasing. Special cases of this cohomological approach generalize results in classical elasticity, e.g., the Korn inequality and the Cesàro-Volterra path integral.
報告人簡介：
胡凱博, 2017 年博士畢業于北京大學. 後在 University of Oslo 和 University of Minnesota 從事博士後研究. 目前研究興趣包括 finite element exterior calculus 及其在連續介質力學和相對論中的應用, 以及有限元和離散幾何/物理的聯系.
