TY - JOUR
T1 - Analysis of an Interaction Problem Between an Electromagnetic Field and an Elastic Body
AU - A. Bernardo, A. Marquez & S. Meddahi
JO - International Journal of Numerical Analysis and Modeling
VL - 4
SP - 749
EP - 765
PY - 2010
DA - 2010/07
SN - 7
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/750.html
KW - Edge finite elements, Maxwell equations and elastodynamics equations.
AB - <p style="text-align: justify;">This paper deals with an interaction problem between a solid and
an electromagnetic field in the frequency domain. More precisely, we aim to
compute both the magnetic component of the scattered wave and the elastic
vibrations that take place in the solid elastic body. To this end, we solve a
transmission problem holding between the bounded domain $\Omega_S \subset R^3$ representing
the obstacle and a sufficiently large annular region surrounding it. We
point out here that (following Voigt&#39;s model, cf. [12]) we only allow the electromagnetic
field to interact with the elastic body through the boundary of

$\Omega_S$. We apply the abstract framework developed in the work [3] by A. Buffa
to prove that our coupled variational formulation is well posed. We define the
corresponding discrete scheme by using the edge element in the electromagnetic
domain and standard Lagrange finite elements in the solid domain. Then we
show that the resulting Galerkin scheme is uniquely solvable, convergent and
we derive optimal error estimates. Finally, we illustrate our analysis with some
results from computational experiments.</p>