Comments on ‘the group velocity of some numerical schemes’

✍ Scribed by Philip M. Gresho; Robert L. Lee

• Publisher: John Wiley and Sons
• Year: 1987
• Tongue: English
• Weight: 256 KB
• Volume: 7
• Category: Article
• ISSN: 0271-2091
• DOI: 10.1002/fld.1650071206

✦ Synopsis

The proper phase and group speeds when quadratic finite elements are applied to the one-dimensional pure advection equation are presented and the myth of a spurious computational mode is dispelled.

KEY WORDS Quadratic Elements FEM Phase Speed Spurious Modes In a very interesting and generally well done paper,' Cathers and O'Connor (hereafter referred to as COC) fell into a common trap regarding the analysis of a finite element method in which quadratic basis functions are employed. Before presenting any details, let us first make clear the major point of this paper: there is no spurious computational mode associated with the quadraticfinite element. In this paper we explain why this is so and also demonstrate the final result numerically.