| 非线性对流扩散方程的双线性元解的高精度分析 |
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| 引用本文： | 石东洋,董晓靖.非线性对流扩散方程的双线性元解的高精度分析[J].天津师范大学学报(自然科学版),2012,32(2):1-5. |
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| 作者姓名： | 石东洋 董晓靖 |
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| 作者单位： | 1. 郑州大学数学系,郑州,450001
2. 郑州大学 教学系,郑州,450001 |
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| 基金项目： | 国家自然科学基金资助项目，高等学校博士学科点专项科研基金资助项目 |
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| 摘 要： | 利用积分恒等式对发展型非线性对流扩散方程的双线性有限元解进行了高精度分析.给出了L2-模意义下的二阶ε一致收敛结果.进一步,根据Bramble-Hilbert引理推导出了2个高精度的积分恒等式,并由此得到了一个新的渐近展开式.
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| 关 键 词： | 非线性对流扩散方程 双线性元 高精度 |
Higher accuracy analysis for bilinear finite element solution of nonlinear advection-diffusion equation |
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| SHI Dong-yang
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DONG Xiao-jing.Higher accuracy analysis for bilinear finite element solution of nonlinear advection-diffusion equation[J].Journal of Tianjin Normal University(Natural Science Edition),2012,32(2):1-5. |
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| Authors: | SHI Dong-yang DONG Xiao-jing |
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| Institution: | Department of Mathematics,Zhengzhou University,Zhengzhou 450001,Chin |
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| Abstract: | By using integral identities,the higher accuracy approximation of bilinear conforming finite element for the time-dependent nonlinear advection-diffusion equations is investigated.The optimal ε uniform convergent result is obtained under L2-norm.Based on Bramble-Hilbert lemma,two new integral identities and a asymptotic error expansion are derived. |
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| Keywords: | nonlinear advection-diffusion equation bilinear finite element higher accuracy |
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