| 非线性四阶双曲方程的非协调有限元分析 |
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| 引用本文： | 陈金环,王黎娜,石东洋.非线性四阶双曲方程的非协调有限元分析[J].河南师范大学学报(自然科学版),2012,40(1):1-6. |
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| 作者姓名： | 陈金环 王黎娜 石东洋 |
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| 作者单位： | 郑州大学数学系,郑州,450052 |
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| 基金项目： | 国家自然科学基金，教育部高等学校博士学科点专项科研基金 |
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| 摘 要： | 讨论了四阶非线性双曲方程在半离散格式下的非协调有限元逼近,借助ACM单元的非协调性,得到了最优误差估计,超逼近和超收敛结果.同时利用Bramble-Hilbert引理,构造了一个新的合适的外推格式,得到了比通常收敛性高一阶的超收敛结果.
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| 关 键 词： | 非线性四阶双曲方程 外推 最优误差估计 超逼近 超收敛 |
A Nonconforming Finite Element for Nonlinear Fourth Order Hyperbolic Equation |
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| CHEN Jin-huan
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WANG Li-na
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SHI Dong-yang.A Nonconforming Finite Element for Nonlinear Fourth Order Hyperbolic Equation[J].Journal of Henan Normal University(Natural Science),2012,40(1):1-6. |
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| Authors: | CHEN Jin-huan WANG Li-na SHI Dong-yang |
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| Institution: | (Department of Mathematics,Zhengzhou University,Zhengzhou 450052,China) |
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| Abstract: | A nonconforming finite element method approximation to nonlinear fourth-order hyperbolic equation is discussed for semi-discrete scheme.Based on the nonconforming property of the ACM’s element,the optimal order error estimates,superclose and superconvergence are derived.At the same time,by virtue of the Bramble-Hilbert lemma,the research has constructed a new and suitable extrapolation scheme and obtained a superconvergence result which is higher one order than the usual convergence. |
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| Keywords: | nonlinear fourth-order hyperbolic equation extrapolation optimal error estimates superclose superconvergence |
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