# 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

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topBécache, 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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