TY  - JOUR
A1  - Eberle, Sarah Maria
T1  - FEM–BEM coupling for the thermoelastic wave equation with transparent boundary conditions in 3D
T2  - Zeitschrift für angewandte Mathematik und Physik
N2  - We consider the thermoelastic wave equation in three dimensions with transparent boundary conditions on a bounded, not necessarily convex domain. In order to solve this problem numerically, we introduce a coupling of the thermoelastic wave equation in the interior domain with time-dependent boundary integral equations. Here, we want to highlight that this type of problem differs from other wave-type problems that dealt with FEM–BEM coupling so far, e.g., the acoustic as well as the elastic wave equation, since our problem consists of coupled partial differential equations involving a vector-valued displacement field and a scalar-valued temperature field. This constitutes a nontrivial challenge which is solved in this paper. Our main focus is on a coercivity property of a Calderón operator for the thermoelastic wave equation in the Laplace domain, which is valid for all complex frequencies in a half-plane. Combining Laplace transform and energy techniques, this coercivity in the frequency domain is used to prove the stability of a fully discrete numerical method in the time domain. The considered numerical method couples finite elements and the leapfrog time-stepping in the interior with boundary elements and convolution quadrature on the boundary. Finally, we present error estimates for the semi- and full discretization.
KW  - Thermoelastic wave equation
KW  - Transparent boundary conditions
KW  - Calderón operator
KW  - Finite elements
KW  - Boundary elements
KW  - Convolution quadrature
KW  - Leapfrog
Y1  - 2022
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/69627
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-696278
SN  - 1420-9039
N1  - Open Access funding enabled and organized by Projekt DEAL.
VL  - 73
IS  - art. 163
SP  - 1
EP  - 27
PB  - Springer International Publishing AG
CY  - Cham (ZG)
ER  -