Analysis For The Superconvergence Of Sobolev Equation

Sobolev equation is widely used in many areas, such as hydromechanics, thermodynamics and so on. There have many works about the finite element solution of the Sobolev equation.Displacement finite element method of the linear Sobolev equation is presented in [5], character mixed finite element method of the Sobolev equation is presented in [9], H 1 ?Galerkinfinite element method is introduced in [7] and least square methods is also mentioned in [10]. Currently, One dimension situation of the corresponding superconvergence is considered, but the research areas about two dimension is blanket. In this paper, the integral identities are used to obtain the approximation of higher accuracy of the mixed finite element and combinatorial finite element on rectangles. The global superconvergence is obtained are also derived. We compared the numerical results of mixed finite element,combined finite element and H 1 ?Galerkin finite element. It is proved that the mixed finite element method has many advantages, the format is simpler and the accuracy is higher.