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Journal Articles SIAM Journal on Numerical Analysis Year : 2009

A new fictitious domain approach inspired by the extended finite element method

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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Dates and versions

hal-00416741 , version 1 (18-01-2019)

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Jaroslav Haslinger, Yves Renard. A new fictitious domain approach inspired by the extended finite element method. SIAM Journal on Numerical Analysis, 2009, 47 (2), pp.1474-1499. ⟨10.1137/070704435⟩. ⟨hal-00416741⟩
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