Superconvergence analysis of an H1-Galerkin mixed finite element method for Sobolev equations

An H-1-Galerkin mixed finite element method (MFEM) is discussed for the Sobolev equations with the bilinear element and zero order Raviart-Thomas element (Q(11) + Q(10) x Q(01)). The existence and uniqueness of the solutions about the approximation scheme are proved. Two new important lemmas are given by using the properties of the integral identity and the Bramble-Hilbert lemma, which lead to the superclose results of order O(h(2)) for original variable u in H-1 norm and flux (q) over right arrow in H(div; Omega) norm under semi-discrete scheme. Furthermore, two new interpolated postprocessing operators are put forward and the corresponding global superconvergence results are obtained. On the other hand, a second order fully-discrete scheme with superclose property O(h(2)+tau(2)) is also proposed. At last, numerical experiment is included to illustrate the feasibility of the proposed method. Here his the subdivision parameter and tau is the time step. (C) 2016 Elsevier Ltd. All rights reserved.