| 一种隐式特征有限元方法的误差估计 |
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| 引用本文： | 窦红. 一种隐式特征有限元方法的误差估计[J]. 安徽大学学报(自然科学版), 2002, 26(2): 40-43. DOI: 10.3969/j.issn.1000-2162.2002.02.008 |
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| 作者姓名： | 窦红 |
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| 作者单位： | 安徽大学数学系,安徽,合肥,230039 |
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| 基金项目： | 安徽省教育厅自然科学基金;2001kj012; |
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| 摘 要： | 特征有限元方法已经被证明比传统的有限元方法能更好地处理对流问题并能取更大的时间步长计算.但目前的特征有限元方法大多是对拟线性标量方程给出.该文给出求解一种二维非线性对流扩散方程组的一个隐式特征有限元方法,利用有限元逼近的理论和方法以及离散Gronwall不等式,证明了该方法的H1模最优阶误差估计.
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| 关 键 词： | 非线性对流扩散方程 特征方法 有限元方法 误差估计 |
| 文章编号： | 1000-2162(2002)02-0040-04 |
Error estimates for an implicit characteristics finite element method |
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| DOU Hong. Error estimates for an implicit characteristics finite element method[J]. Journal of Anhui University(Natural Sciences), 2002, 26(2): 40-43. DOI: 10.3969/j.issn.1000-2162.2002.02.008 |
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| Authors: | DOU Hong |
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| Abstract: | Characteristic methods are known to handle advection flow better than traditional Galerkin methods and allow large time steps to be taken when compared to standard time-stepping methods. However, the mostly existed characteristic methods are the schemes for the quasilinear scalar equations. In the paper, an implicit characteristics finite element method for a kind of 2-dimensional nonlinear system of convection-diffusion equations is proposed. Using the theory and method of the finite element approximation and the discrete Gronwall's inequality, the optimal error estimates in H 1 norm is derived. |
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| Keywords: | convection-diffusion euqations characteristics method Galerkin finite element method error estimates |
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