Volume 43, Number 2, March-April 2009
|Page(s)||377 - 398|
|Published online||05 December 2008|
Convergence results of the fictitious domain method for a mixed formulation of the wave equation with a Neumann boundary condition
POEMS, INRIA-Rocquencourt, BP 105, 78153 Le
Chesnay Cédex, France. firstname.lastname@example.org
2 POEMS, ENSTA, 32 boulevard Victor, 75739 Paris Cedex 15, France. email@example.com
3 Dept. of Applied Mathematics, University of Crete & IACM/FORTH, Crete, Greece. firstname.lastname@example.org
Revised: 22 September 2008
The problem of modeling acoustic waves scattered by an object with Neumann boundary condition is considered. The boundary condition is taken into account by means of the fictitious domain method, yielding a first order in time mixed variational formulation for the problem. The resulting system is discretized with two families of mixed finite elements that are compatible with mass lumping. We present numerical results illustrating that the Neumann boundary condition on the object is not always correctly taken into account when the first family of mixed finite elements is used. We, therefore, introduce the second family of mixed finite elements for which a theoretical convergence analysis is presented and error estimates are obtained. A numerical study of the convergence is also considered for a particular object geometry which shows that our theoretical error estimates are optimal.
Mathematics Subject Classification: 65M60 / 65M12 / 65M15 / 65C20 / 74S05
Key words: Mixed finite elements / fictitious domain method / domain embedding method / acoustic waves / convergence analysis.
© EDP Sciences, SMAI, 2009
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.