(untitled) (Journal of Computational Mathematics, 2019)
An H^1-Galerkin mixed finite element method (MFEM) is discussed for the two-dimensional Ginzburg-Landau equation with the bilinear element and zero order Raviart-Thomas element (Q_11 + Q_10 × Q_01). A linearized Crank-Nicolson fully-discrete scheme is developed and a time-discrete system is introduced to split the error into two parts which are called the temporal error and the spatial error, respectively. On one hand, the regularity of the time-discrete system is deduced through the temporal error estimation. On the other hand, the superconvergent estimates of u in H^1-norm and q in H(div; Ω)-norm with order O(h^2 + τ^2) are obtained unconditionally based on the achievement of the spatial result. At last, a numerical experiment is included to illustrate the feasibility of the proposed method. Here, h is the subdivision parameter and τ is the time step.