Analysis Of Nonstandard Schemes For Mixed Finite Element Methods

In this paper, we focus on convergence and superconvergence analysis of two nonstan-dard mixed finite element methods. Firstly, we consider the applications of Least-Squares nonconforming mixed finite element methods for the second elliptic problems. Since the speciality of the scheme, we discuss the case that the approximation space of the exact solution is the so-called five-nodes nonconforming space and one of flux is the lowest order Raviart-Thomas space. By means of the novel techniques, we obtain the same convergence as the traditional methods. And we also derive the global superconvergence of the exact solution using the novel skill and the postprocessing trick.Secondly, we study the nonconforming H1-Galerkin mixed finite element methods of evolution equations. Similarly, using the same nonconforming mixed finite element spaces as ones of the second chapter, the same convergence as the traditional methods is obtained without the Ritz or Ritz-Volterra projection. And we also derive the global superconvergence of the exact solution using the postprocessing technique. Finally, we discuss the superclose of the full discrete scheme of the Sobolev equation using the H1-Galerkin mixed finite element methods.