IJPAM: Volume 4, No. 1 (2003)

NUMERICAL EXPERIMENTS WITH THE MOVING
FINITE ELEMENT METHOD

A. Vande Wouwer$^1$, P. Saucez$^2$, W.E. Schiesser$^3$
$^1$Laboratoire d'Automatique
Faculté Polytechnique de Mons
Boulevard Dolez, 31B-7000, Mons, BELGIUM
e-mail: vdw@autom.fpms.ac.be
$^2$Service de Mathématique
Faculté Polytechnique de Mons, BELGIUM
$^{3}$Mathematics and Engineering
Lehigh University, USA


Abstract.Since its invention by K. Miller, the moving finite element (MFE) method has been the subject of continuing investigations and developments. However, because of the usual lag between research and applications, the MFE method, and its several variants, can still be sensitive to the approach and use by the non-specialist.

This paper presents the results of a series of numerical experiments aimed at assessing, from a user's point of view, the influence of several of the method's features. These include the choice of regularizing parameters, the selection of the initial node distribution, the use of gradient weighting (GWMFE), as well as some issues relating to the numerical evaluation of the PDE residuals, time integration and the use of diagonal preconditioning.

A few classical 1-D test examples, which can be solved successfully with the MFE and GWMFE methods, are used to highlight these several points. In addition, some more difficult PDE systems are used to illustrate limitations and potential failures of the method.

Received: March 3, 2002

AMS Subject Classification: 65M20, 65M50, 65M60

Key Words and Phrases: partial differential equations, method of lines, combustion, gas dynamics, Schroedinger equation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2003
Volume: 4
Issue: 1