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一阶线性双曲方程的耗散谱元法 被引量：1

Dissipative spectral element method for first-order linear hyperbolic equation
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摘要 讨论了二维一阶线性变系数双曲方程的耗散谱元法,得到拟最优估计.数值结果表明,耗散谱元法对于具有较复杂边界条件的问题同样有效,对于有限光滑问题,耗散谱元法能够得到比传统的谱元法更好的结果. The dissipative spectral element method for the two dimensional first- order linear variable coefficients hyperbolic equation is discussed in this paper. Quasi-optimal error estimate is obtained for the scheme. Numerical results verify the validity of the underlying scheme in dealing with complex boundary conditions and its some superiority over the standard spectral element method for the solutions of the limited smoothness.
作者 陈炼 马和平
机构地区 上海大学理学院 上海应用技术学院理学院
出处 《应用数学与计算数学学报》 2013年第4期491-500,共10页 Communication on Applied Mathematics and Computation
基金 国家自然科学基金资助项目(11171209) 上海市教育委员会重点学科建设资助项目(J50101) 上海大学研究生创新基金资助项目(SHUCX091048)
关键词 一阶线性双曲方程 耗散 谱元法 first-order linear hyperbolic equation dissipative spectral elementmethod
分类号 O241.82 [理学—计算数学]
  • 相关文献

参考文献10

  • 1Canuto C, Hussaini M Y, Quarteroni A, Zang T A. Spectral Methods: Fundamentals in Single Domains [M]. Berlin: Springer-Verlag, 2006.
  • 2Shen J, Wang L L. Legendre and Chebyshev dual-Petrov-Galerkin methods for hyperbolic equations[J]. Comput Methods Appl Mech Engrg, 2007, 196(37/38/39/40): 3785-3797.
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  • 4Dendy J E. Two methods of Galerkin type achieving optimum L2 rates of convergence for first order hyperbolics [J]. SIAM J Numer Anal, 1974, 11(3): 637-653.
  • 5Wahlbin L B. A dissipative Galerkin method for the numerical solution of first-order hyperbolic equation [M]/ / Mathematical Aspects of Finite Elements in Partial Differential Equations. New York: Academic Press, 1974: 147-169.
  • 6Wahlbin L B. A dissipative Galerkin method applied to some quasilinear hyperbolic equations [J]. Revue Francaise D'automatique, Informatique, Recherche Operationnelle. Analyse Numerique, 1974, 8(2): 109-117.
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  • 8杨征,张中强.一阶双曲方程的耗散谱tau方法及最优误差估计[J].丽水学院学报,2008,30(5):12-15. 被引量：2
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二级参考文献6

  • 1Ma H P,Sun W W. A Legendre-Petrov-Galerkin and Chebyshev collocation method for third order differential equations[J]. SIAM Journal on Numerical Analysis, 2000,38:1 425-1 438.
  • 2Ma H P,Sun W W. Optimal error estimates of the Legendre-Petrov-Galerkin method for the Korteweg-de Vries equation[J]. SIAM Jour nal on Numerical Analysis,2001,39:1 380-1 394.
  • 3Shen J. A new dual-Petrov-Galerkin method for third and higher odd-order differential equations: Application to the KdV equation[J]. SIAM Journal on Numerical Analysis, 2003,41 : 1595- 1619.
  • 4Dendy J E. Two methods of Galerkin type achieving optimum l^2 rates of convergence for first order hyperbolics[J]. SIAM Journal of Numerical Analysis, 1974,11 : 637-653.
  • 5Shen J. Wang L L. Legendre and chebyshev dual-petrov-galerkin methods for hyperbolic equations[J]. Computer Methods in Applied Mechanics and Engineering,2007,196:3 785-3 797.
  • 6Canuto C, Hussaini M Y, Quartesoni A, et al. Spect ral Methods in Fluid Dynamics[ M]. Berlin Springer Verlag, 1988.

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应用数学与计算数学学报
2013年 第4期

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