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

✍ Scribed by Jie Shen; Li-Lian Wang

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 318 KB
• Volume: 196
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/j.cma.2006.10.031

✦ Synopsis

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.