非线性对流-扩散方程的多区域拟谱方法

纪园园; 吴华; 马和平; 郭本瑜

doi:10.3879/j.issn.1000-0887.2011.10.004

非线性对流-扩散方程的多区域拟谱方法

doi: 10.3879/j.issn.1000-0887.2011.10.004

上海大学数学系, 上海 200444;

基金项目: 国家自然科学基金资助项目(60874039);上海市教委重点学科建设资助项目(J50101)

详细信息

作者简介:
纪园园(1984- ),女,河北保定安国人,硕士(E-mail:jiyuanyuan100@163.com);马和平,教授,博士,博士生导师(联系人.Tel:+86-21-66134331;E-mail:hpma@shu.edu.cn).

中图分类号: O241.82
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出版历程
- 收稿日期: 2011-05-18
- 修回日期: 2011-07-28
- 刊出日期: 2011-10-15

Multidomain Pseudospectral Methods for Nonlinear Convection-Diffusion Equations

Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China;
Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China

摘要

摘要: 提出了非线性对流-扩散方程的多区域拟谱方法．在每个子区间上,该格式整体上按Legendre－Galerkin方法形成,但对于非线性项采用在 Legendre/Chebyshev－Gauss-Lobatto点上的配置法处理．通过选取适当的基函数,使得系数矩阵稀疏,并且可以并行计算,提高运算效率．给出了该方法的稳定性和收敛性分析,获得了按L2-模的最佳误差估计．最后给出单区域和多区域方法的数值算例,并加以比较．
- 多区域 /
- Legendre/Chebyshev配置 /
- 对流-扩散方程
Abstract: Multidomain pseudospectral approximations to nonlinear convection-diffusion equations were considered.The schemes were formulated in the Legendre-Galerkin method but the nonlinear term was collocated at the Legendre/Chebyshev-Gauss-Lobatto points inside each subinterval.Appropriate base functions were introduced so that the matrix of system was sparse and the method can be implemented efficiently and in parallel.The stability and the optimal rate of convergence of the methods were proved.Numerical results were given for both the single domain and the multidomain methods to make a comparison.
- multidomain /
- Legendre/Chebyshev collocation /
- convection-diffusion equation

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参考文献(16)

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