A Petrov-Galerkin finite element scheme for the regularized long wave equation

• Type: Article in International Scientific Journal
• Date: 2004

Authors

Paulo Avilez Valente (Author) FEUP; F. J. Seabra Santos (Author) Other

Journal

Title: Computational Mechanics

Vol. 34 No. 4

Pages: 256-270

ISSN: 0178-7675

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 38 Citations

ISI Web of Science

Scopus - 41 Citations

COMPENDEX

Scientific classification

CORDIS: Physical sciences > Mathematics ; Technological sciences > Engineering

Other information

Authenticus ID: P-000-8NA

DOI: 10.1007/s00466-004-0570-4

Abstract (EN): A Petrov-Galerkin finite element method (FEM) for the regularized long wave (RLW) equation is proposed. Finite elements are used in both the space and the time domains. Dispersion correction and a highly selective dissipation mechanism are introduced through additional streamline upwind terms in the weight functions. An implicit, conditionally stable, one-step predictor-corrector time integration scheme results. The accuracy and stability are investigated by means of local expansion by Taylor series and the resulting equivalent differential equation. An analysis based on a linear Fourier series solution and the Von Neumann's stability criterion is also performed. Based on the order of the analytical approximations and of the domain discretization it is concluded that the scheme is of third order in the nonlinear version and of fourth order in the linear version. Three numerical experiments of wave propagation are presented and their results compared with similar ones in the literature: solitary wave propagation, undular bore propagation, and cnoidal wave propagation. It is concluded that the present scheme possesses superior conservation and accuracy properties.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 15