Convergence results of the fictitious domain method for a mixed formulation of the wave equation with a Neumann boundary condition - Archive ouverte HAL Access content directly
Journal Articles ESAIM: Mathematical Modelling and Numerical Analysis Year : 2009

Convergence results of the fictitious domain method for a mixed formulation of the wave equation with a Neumann boundary condition

Abstract

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. © 2009 EDP Sciences SMAI.

Dates and versions

hal-00873073 , version 1 (17-10-2013)

Identifiers

Cite

Eliane Bécache, Jerónimo Rodríguez, Chrysoula Tsogka. Convergence results of the fictitious domain method for a mixed formulation of the wave equation with a Neumann boundary condition. ESAIM: Mathematical Modelling and Numerical Analysis, 2009, 43 (2), pp.377-398. ⟨10.1051/m2an:2008047⟩. ⟨hal-00873073⟩
184 View
0 Download

Altmetric

Share

Gmail Facebook X LinkedIn More