| 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 |
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| 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 |
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| 作者姓名： | 李先枝 范中广 |
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| 作者单位： | 1.郑州师范学院 |
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| 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.
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| 关 键 词： | 外推. |
| 收稿时间： | 2017-12-14 |
| 修稿时间： | 2018-03-25 |
High Accuracy Analysis of Hermite-type Finite Element for Nonlinear Parabolic Integro-differential Equations |
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| 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 |
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| Authors: | LI Xianzhi FAN Zhongguang |
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| 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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| Keywords: | extrapolation. |
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