Abstract
We consider the FEM-BEM coupling for two special wave-type equations: the acoustic and the elastic wave equation. In more detail, we take a look at the coupling of the interior and exterior problems of these wave-type equations and review a stable numerical method including the corresponding error estimates as well as the convergence. The intent of this paper is to thereby highlight the similarities, while at the same time presenting the challenges inherent in switching from the scalar acoustic to the vectorial elastic equation.
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References
Abboud, T., Joly, P., Rodriguez, J., Terrasse, I.: Coupling discontinuous Galerkin methods and retarded potentials for transient wave propagation on unbounded domains. J. Comput. Phys. 230(15), 5877–5907 (2011)
Augustin, M., Eberle, S.: FEM-BEM coupling for the thermoelastic wave equation with transparent boundary conditions in 3d. (submitted)
Banjai, L., Lubich, Ch., Sayas, F.J.: Stable numerical coupling of exterior and interior problems for the wave equation. Numer. Math. 129, 611–646 (2015)
Eberle, S.: The elastic wave equation and the stable numerical coupling of its interior and exterior problems. Z. Angew. Math. Mech. 98, 1261–1283 (2018)
Eberle, S.: An implementation and numerical experiments of the FEM-BEM coupling for the elastodynamic wave equation in 3d. Z. Angew. Math. Mech. 99(12), (2019)
Kovács, B., Lubich, Ch.: Stable and convergent fully discrete interior-exterior coupling of Maxwell’s equations. Numer. Math. 137, 91–117 (2017)
Lubich, Ch.: Convolution quadrature and discretized operational calculus. I. Numer. Math. 52(2), 129–145 (1988)
Lubich, Ch.: Convolution quadrature and discretized operational calculus. II. Numer. Math. 52(2), 413–425 (1988)
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The author would like to thank the anonymous reviewer for the helpful remarks and suggestions for the improvement of the paper.
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Eberle, S. (2020). FEM-BEM Coupling of Wave-Type Equations: From the Acoustic to the Elastic Wave Equation. In: Dörfler, W., et al. Mathematics of Wave Phenomena. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-47174-3_7
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DOI: https://doi.org/10.1007/978-3-030-47174-3_7
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