On Nonsmooth Solutions of Linear Hyperbolic Systems

✍ Scribed by Knut S. Eckhoff; Jens H. Rolfsnes

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 437 KB
• Volume: 125
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1996.0075

✦ Synopsis

discontinuous initial values associated with (1), we have to consider generalized solutions in the form of generalized Initial value problems for linear hyperbolic systems with smooth 2ȏ-periodic coefficients are solved numerically by a modified Fou-functions (or distributions) [5; 6; 4, Appendix A]. In this rier-Galerkin method when the initial values are nonsmooth. The paper, however, the generalized solutions considered for described approach is seen to give substantially improved accuracy

(1) will for each t be assumed to be piecewise smooth with compared to more traditional methods. The discontinuities are accurespect to x.

rately resolved already on coarse grids, and the fine-structure of Utilizing Fourier methods, numerical solutions of (1) structured solutions is resolved on relatively coarse grids as well.

subject to discontinuous initial data have been studied, for

The accuracy is seen to be of high order and, even for very long term integrations, the global error can be kept very small if the grid instance by Majda et al. [17]. In [17] it was proved that by is sufficiently refined.