A least-squares finite element scheme for the RLW equation

Gardner L. R., Gardner G., DOĞAN A.

COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING, vol.12, no.11, pp.795-804, 1996 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 11
  • Publication Date: 1996
  • Journal Name: COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.795-804
  • Keywords: RLW equation, finite element methods, Petrov-Galerkin, LONG-WAVE EQUATION
  • Abdullah Gül University Affiliated: Yes

Abstract

The RLW equation is solved by a least-squares technique using linear space-time finite elements. In simulations of the migration of a single solitary wave this algorithm is shown to have higher accuracy and better conservation than a recent difference scheme based on cubic spline interpolation functions. In addition, for very small amplitude waves (less than or equal to 0.09) it has higher accuracy than an approach using quadratic B-spline finite elements within Galerkin's method. The development of an undular bore is modelled.