講座主題：Conforming Finite Element Gradgrad and Divdiv Complexes
專(zhuān)家姓名：胡俊
工作單位：北京大學(xué)數(shù)學(xué)科學(xué)學(xué)院
講座時(shí)間：2022年11月6日 14:00-16:00
講座地點(diǎn)：騰訊會(huì)議：136-909-473
主辦單位：煙臺(tái)大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院
內(nèi)容摘要：
We focus on two families of Hilbert complexes which are related to the stable mixed finite element method for the linearized Einstein-Bianchi system: the gradgrad complex and the divdiv complex. We first construct the exact discrete gradgrad complex. There are three main results of this part: (i) an intrinsic structure of the symmetric H(curl) elements; (ii) an intrinsic structure of the traceless H(div) elements; (iii) explicit expressions of the H(curl) and H(div) bubble spaces. We also present the first family of conforming finite element divdiv complexes. In these complexes, the symmetric H(divdiv) elements are from existing literature, while the finite elements of both H(sym curl) and H1 are newly constructed here. It is proved that these finite element complexes are exact. As a results, these spaces can be used in the mixed form of the linearized Einstein-Bianchi system.
主講人介紹：
胡俊，北京大學(xué)數(shù)學(xué)科學(xué)學(xué)院教授，主要從事非標(biāo)準(zhǔn)有限元方法的研究，（與合作者）建立了一個(gè)設(shè)計(jì)線(xiàn)彈性力學(xué)問(wèn)題混合有限元方法的新框架, 構(gòu)造了以多項(xiàng)式為形函數(shù)、應(yīng)力嚴(yán)格對(duì)稱(chēng)、有最優(yōu)收斂性的穩(wěn)定混合有限元，并在此基礎(chǔ)上設(shè)計(jì)了四階問(wèn)題內(nèi)蘊(yùn)的混合有限元方法；首次構(gòu)造出線(xiàn)性化Einstein-Bianchi方程組兩族保結(jié)構(gòu)的穩(wěn)定混合有限元方法。曾獲國(guó)家杰出青年科學(xué)基金、馮康科學(xué)計(jì)算獎(jiǎng)、中國(guó)數(shù)學(xué)會(huì)計(jì)算數(shù)學(xué)分會(huì)首屆青年創(chuàng)新獎(jiǎng)?，F(xiàn)任期刊Adv.Appl.Math.Mech.執(zhí)行主編、期刊Comput. Math. Appl.,Comput. Methods Appl. Math.，CSIAM Trans. Appl. Math.， J.Comput.Math.和數(shù)學(xué)理論與應(yīng)用的編委、北京計(jì)算數(shù)學(xué)學(xué)會(huì)理事長(zhǎng)、中國(guó)數(shù)學(xué)會(huì)常務(wù)理事、中國(guó)大壩工程學(xué)會(huì)大壩數(shù)值模擬專(zhuān)業(yè)委員會(huì)副主任委員，中國(guó)數(shù)學(xué)會(huì)計(jì)算數(shù)學(xué)分會(huì)理事。
