IJPAM: Volume 4, No. 1 (2003)
FINITE ELEMENT METHOD
Faculté Polytechnique de Mons
Boulevard Dolez, 31B-7000, Mons, BELGIUM
Service de Mathématique
Faculté Polytechnique de Mons, BELGIUM
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