The Investigation Of Electromagnetic Systems Approximated By Nonconforming Finite Element

In this thesis,new nonconforming mixed finite element spaces are presented.The first,only using the traditional discrete form can establish a robust appoach method to solve time-depend Maxwell equations. Where numerical examples are given to verify the theoretical analysis in convex and non-conver domains. The second,to implement our theory for the wave propagation in metamaterials in the three dimensional. The error estimate of the semi-discrete scheme is given by cinvergence O(h).A Grank-Nicolson full discrete scheme is provided with convergence order O(τ2 + h). Finally,numerical examples of TE case to verify our theories.The most important contribution in this thesis,(1) Only curl conforming by the means of integration continuity in stead of function continuity is needed;(2) The commutative rule between interpolation operator and di?erential operator holds;(3) The jumps of unit outer normal vector can be controlled based on the properties of nonconforming finite element;(4) The traditional discrete scheme is employed without needing penalty technique;(5) The finite element space is divergence free.