New Finite element  methods for fourth order curl-problems
Bin Zheng

Abstract: The goal of this talk is to present some results on the finite element approximations of fourth order curl-equations (involving curl^4) arising from magnetohydrodynamics (MHD) models. I will briefly discuss several difficulties encountered in the finite element approximations of biharmonic equations and especially the fourth order curl^4-equations. Then, I will present two newly constructed nonconforming finite elements for the fourth order curl^4 equations in three dimensions.  Attactive properties of these elements include the use of a small number of degrees of freedom and the imposed tangential inter-element continuity which is appropriate for the approximation of magnetic field. I will also present some details on the construction of basis functions as well as the convergence analysis.