李先枝, 范中广. 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[J]. 华南师范大学学报(自然科学版), 2019, 51(2): 98-104. doi: 10.6054/j.jscnun.2019032
引用本文: 李先枝, 范中广. 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[J]. 华南师范大学学报(自然科学版), 2019, 51(2): 98-104. doi: 10.6054/j.jscnun.2019032
LI Xianzhi, FAN Zhongguang. High Accuracy Analysis of Hermite-type Finite Element for Nonlinear Parabolic Integro-differential Equations[J]. Journal of South China Normal University (Natural Science Edition), 2019, 51(2): 98-104. doi: 10.6054/j.jscnun.2019032
Citation: LI Xianzhi, FAN Zhongguang. High Accuracy Analysis of Hermite-type Finite Element for Nonlinear Parabolic Integro-differential Equations[J]. Journal of South China Normal University (Natural Science Edition), 2019, 51(2): 98-104. doi: 10.6054/j.jscnun.2019032

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.

     

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