High Accuracy Analysis of Hermite-type Finite Element for Nonlinear Parabolic Integro-differential Equations

A Hermite-type finite element method is discussed for nonlinear parabolic integro-differential equations. The superclose and the order global superconvergence result for semi-discrete scheme is obtained by use of high accuracy analysis of the element, mean-value theorem and the derivative transfer techniques. At the same time, the fourth-order extrapolation solution is deduced through constructing a suitable extrapolation scheme.