Legendre and Chebyshev dual-Petrov–Galerkin methods for Hyperbolic equations

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• 作者：Jie Shen ; Li-Lian Wang
• 关键词：Legendre polynomials ; Chebyshev polynomials ; Spectral and pseudo-spectral approximations ; Hyperbolic problems ; Dual-Petrov– ; Galerkin method
• 刊名：Computer Methods in Applied Mechanics and Engineering
• 出版年：2007
• 期刊代码：27_00457825
• 类别：cp
• 出版时间：1 August 2007
• 卷：196
• 期：37-40
• 页码：3785-3797
• 文件大小：318 K

摘要

A Legendre and Chebyshev dual-Petrov–Galerkin method for hyperbolic equations is introduced and analyzed. The dual-Petrov–Galerkin method is based on a natural variational formulation for hyperbolic equations. Consequently, it enjoys some advantages which are not available for methods based on other formulations. More precisely, it is shown that (i) the dual-Petrov–Galerkin method is always stable without any restriction on the coefficients; (ii) it leads to sharper error estimates which are made possible by using the optimal approximation results developed here with respect to some generalized Jacobi polynomials; (iii) one can build an optimal preconditioner for an implicit time discretization of general hyperbolic equations.