An adaptive enrichment algorithm for advection-dominated problems
Article first published online: 9 NOV 2012
Copyright © 2012 John Wiley & Sons, Ltd.
International Journal for Numerical Methods in Fluids
Volume 72, Issue 3, pages 359–374, 30 May 2013
How to Cite
Abgrall, R. and Krust, A. (2013), An adaptive enrichment algorithm for advection-dominated problems. Int. J. Numer. Meth. Fluids, 72: 359–374. doi: 10.1002/fld.3745
- Issue published online: 17 APR 2013
- Article first published online: 9 NOV 2012
- Manuscript Accepted: 25 SEP 2012
- Manuscript Revised: 21 SEP 2012
- Manuscript Received: 26 MAR 2012
- FP7 ERC Advanced Research. Grant Number: 226316 ADDECCO
- stabilized finite elements;
- discrete enrichment method;
We are interested in developing a numerical framework well suited for advection–diffusion problems when the advection part is dominant. In that case, given Dirichlet type boundary condition, it is well known that a boundary layer develops. To resolve correctly this layer, standard methods consist in increasing the mesh resolution and possibly increasing the formal accuracy of the numerical method. In this paper, we follow another path: we do not seek to increase the formal accuracy of the scheme but, by a careful choice of finite element, to lower the mesh resolution in the layer. Indeed the finite element representation we choose is locally the sum of a standard one plus an enrichment. This paper proposes such a method and with several numerical examples, we show the potential of this approach. In particular, we show that the method is not very sensitive to the choice of the enrichment and develop an adaptive algorithm to automatically choose the enrichment functions.Copyright © 2012 John Wiley & Sons, Ltd.