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

Eliane Bécache; Jeronimo Rodríguez; Chrysoula Tsogka

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

  • Volume: 43, Issue: 2, page 377-398
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Bécache, Eliane, Rodríguez, Jeronimo, and Tsogka, Chrysoula. "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 43.2 (2008): 377-398. <http://eudml.org/doc/194455>.

@article{Bécache2008,
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. },
author = {Bécache, Eliane, Rodríguez, Jeronimo, Tsogka, Chrysoula},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Mixed finite elements; fictitious domain method; domain embedding method; acoustic waves; convergence analysis.; mixed finite elements; convergence; numerical results; error estimates},
language = {eng},
month = {12},
number = {2},
pages = {377-398},
publisher = {EDP Sciences},
title = {Convergence results of the fictitious domain method for a mixed formulation of the wave equation with a Neumann boundary condition},
url = {http://eudml.org/doc/194455},
volume = {43},
year = {2008},
}

TY - JOUR
AU - Bécache, Eliane
AU - Rodríguez, Jeronimo
AU - Tsogka, Chrysoula
TI - Convergence results of the fictitious domain method for a mixed formulation of the wave equation with a Neumann boundary condition
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2008/12//
PB - EDP Sciences
VL - 43
IS - 2
SP - 377
EP - 398
AB - 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.
LA - eng
KW - Mixed finite elements; fictitious domain method; domain embedding method; acoustic waves; convergence analysis.; mixed finite elements; convergence; numerical results; error estimates
UR - http://eudml.org/doc/194455
ER -

References

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