Speaker: Zhiming Zhang

Affiliation: Wayne State U

Title: Construction of H²(curl) conforming elements and their application

Abstract: In 1980 and 1986, Nedelec proposed H(curl)-conforming elements to solve electromagnetic equations that contains the “curl” operator. It is more or less as the H¹-conforming elements (or C⁰ elements) for elliptic equations that contains the “grad” operator. As is well known in the finite element method literature, in order to solve 4^th-order elliptic equations such as the bi-harmonic equation, H²-conforming elements (or C⁰-elements) were developed. Recently, there have been some research in solving electromagnetic equations which involve four “curl” operators. Hence, construction of H(curl curl)-conforming elements becomes necessary. In this work, we construct H(curl curl)-conforming elements for rectangular and triangular meshes and apply them to solve quad-curl equations as well as related eigenvalue problems.