Superconvergence of an H1H1-Galerkin nonconforming mixed finite element method for a parabolic equation

By choosing a suitable pair of approximating spaces, an H1H1-Galerkin nonconforming mixed finite element method (FEM) is proposed for a class of parabolic equations under semi-discrete, backward Euler and Crank–Nicolson fully-discrete schemes, in which the famous EQ1rot element and zero order Raviart–Thomas element are used to approximate the primitive solution uu and the flux p→=∇u, respectively. Based on special characters of the elements considered, the corresponding optimal order error estimates for uu in broken H1H1-norm and p→ in H(div)H(div)-norm are obtained for the above schemes. Furthermore, the global superconvergence results are derived through the postprocessing technique. The numerical results show the validity of the theoretical analysis.