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A NEW FICTITIOUS DOMAIN APPROACH INSPIRED BY THE EXTENDED FINITE ELEMENT METHOD

JAROSLAV HASLINGER and YVES RENARD
SIAM Journal on Numerical Analysis
Vol. 47, No. 2 (2009), pp. 1474-1499
Stable URL: http://www.jstor.org/stable/25663177
Page Count: 26
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A NEW FICTITIOUS DOMAIN APPROACH INSPIRED BY THE EXTENDED FINITE ELEMENT METHOD
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Abstract

The purpose of this paper is to present a new fictitious domain approach inspired by the extended finite element method introduced by Moës, Dolbow, and Belytschko in [Internat. J. Numer. Methods Engrg., 46 (1999), pp. 131–150]. An optimal method is obtained thanks to an additional stabilization technique. Some a priori estimates are established and numerical experiments illustrate different aspects of the method. The presentation is made on a simple Poisson problem with mixed Neumann and Dirichlet boundary conditions. The extension to other problems or boundary conditions is quite straightforward.

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