Finite Element De Rham Complexes

主講人：黃學海 上海財經(jīng)大學講席教授

時間：2023年12月21日14：00

地點：三號樓301室

舉辦單位：數(shù)理學院

主講人介紹：黃學海，上海財經(jīng)大學講席教授、博士研究生導師，研究方向為有限元方法。在Math. Comp.、SIAM J. Numer. Anal.、Numer. Math.、Math. Models Methods Appl. Sci.等國際期刊發(fā)表SCI 論文四十多篇。正主持一項國家自然科學基金面上項目和上海市自然科學基金原創(chuàng)探索項目,主持完成國家自然科學基金面上項目、青年項目、數(shù)學天元項目和溫州市科技計劃項目各一項、浙江省自然科學基金項目兩項。獲中國計算數(shù)學學會優(yōu)秀青年論文競賽優(yōu)秀獎，博士學位論文被評為上海市研究生優(yōu)秀成果(學位論文)。

內(nèi)容介紹：The construction of finite element De Rham complexes is presented in this talk. The polynomial De Rham complex and Koszul complex are combined to derive the decompositions of vectorial polynomial spaces. Traces of H(div) and H(curl) are shown. Different ways of constructing H(div)-conforming finite elements and H(curl)-conforming finite elements are discussed. Especially, with the help of the geometric decomposition and the tangential-normal decomposition, the basis functions of Lagrange element can be used to form the basis functions of H(div)-conforming finite elements and H(curl)-conforming finite elements, whose implementation is easy.