非线性抛物积分微分方程非常规Hermite型矩形元的高精度分析
High Accuracy Analysis of Hermite-type Finite Element for Nonlinear Parabolic Integro-differential Equations
-
摘要: 讨论一类非线性抛物积分微分方程的Hermite有限元方法,利用该元的性质,平均值技巧和导数转移技巧,得到了半离散格式的超逼近性质和相应的超收敛结果, 并通过构造一个合适的外推格式得到了具有四阶精度的外推解.Abstract: 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.