An H~1-Galerkin Mixed Element Method For Fourth-order Parabolic Integral Differential Equations

In this paper, an H1-Galerkin mixed element method is studied and discussed for a class of evolution integral differential equation with fourth-order derivatives in space, the error estimates in both one-dimensional case and multi-dimensional case are derived.In the part Ⅰ, an H1-Galerkin mixed element method is considered for one-dimensional fourth-order integro-differential equation of parabolic type. According to the character-istics of the considered equation, the three auxiliary variables are introduced, then the original fourth-order problem can be split into the coupled system with first order deriva-tive. Some optimal error estimates for both semi-and fully discrete scheme are proved and the stability for fully discrete system is also derived.In the part Ⅱ, the parabolic fourth-order integro-differential equation in multidimen-sional case is also analyzed by the H1-Galerkin mixed element method, and the a priori error estimates for semi-discrete system are discussed.