The Studies Of Crouzeix-Raviart Nonconforming FEMs Approximation For Maxwell’s Problems

In this thesis,we consider Maxwell problems(including two-dimensional mixed Maxwell’s equations and curl-curl problems) approximated by Crouzeix-Raviart nonconforming finite el-ement methods and discontinuous Galerkin methods,respectively.By establishing new discrete forms and norms,we provide the convergence analysis with different techniques.Firstly,we employ Helmholtz decomposition to devide the mixed time-harmonic Maxwell problems into two different problems whose solutions are unique.By introducing the new dis-crete variational format and its corresponding norm,we build the Strang lemma and convergence analysis.At the same time,the numerical experiments are carried to verify our theoretical result-s.Then,inspired by the discontinuous Galerkin methods,we propose interior penalty discontinu-ous Galerkin methods to curl-curl equations.We establish the new discontinuous Galerkin dis-crete form and the new norm to present Strang lemmas and the error estimates.Furthemore,we prove our theoretical result by some numerical experiments.