Superconvergence Analysis Of Finite Element Methods For Two Kinds Of The Development Of Equations

This paper mainly includes two parts.In the first part,the bilinear finite element method with moving grid is studied for a kind of nonlinear hyperbolic equations.Based on the special properties of elemen-t's interpolation instead of the traditional Ritz projection,together with the derivative transfer technique ,the super convergence result is deduced under the time step restric-tion ?t = O(h2).In the second part ,a novel Crank-Nicolson least squares mixed finite element method (FEM) is considered for the parabolic integro-differential equation, in which the nonconforming Q1rot element and the lowest order rectangular Raviart-Thomas (R-T) element are used to approximate the primitive solution u and the flux ?, respectively.By use of the typical characters of these two elements, the superconvergence error esti-mates of u in broken H1-norm and ? in L2-norm are obtained, respectively. At the same time, a numerical experiment is carried out to confirm the theoretical results.