Time accurate consistently stabilized mesh-free methods for convection dominated problems
Article first published online: 3 JAN 2003
Copyright © 2003 John Wiley & Sons, Ltd.
International Journal for Numerical Methods in Engineering
Volume 56, Issue 9, pages 1225–1242, 7 March 2003
How to Cite
Huerta, A. and Fernández-Méndez, S. (2003), Time accurate consistently stabilized mesh-free methods for convection dominated problems. Int. J. Numer. Meth. Engng., 56: 1225–1242. doi: 10.1002/nme.602
- Issue published online: 3 JAN 2003
- Article first published online: 3 JAN 2003
- Manuscript Accepted: 2 MAY 2002
- Manuscript Revised: 8 APR 2002
- Manuscript Received: 5 NOV 2001
- Ministerio Ciencia y Tecnología. Grant Number: REN2001-0925-C03-01
- finite elements;
- stream-line-upwind Petrov–Galerkin
The behaviour of high-order time stepping methods combined with mesh-free methods is studied for the transient convection–diffusion equation. Particle methods, such as the element-free Galerkin (EFG) method, allow to easily increase the order of consistency and, thus, to formulate high-order schemes in space and time. Moreover, second derivatives of the EFG shape functions can be constructed with a low extra cost and are well defined, even for linear interpolation. Thus, consistent stabilization schemes can be considered without loss in the convergence rates. Copyright © 2003 John Wiley & Sons, Ltd.