A unified error analysis for nonlinear wave-type equations with application to acoustic boundary conditions
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Published:2022-10-31
Issue:4
Volume:152
Page:907-936
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ISSN:0029-599X
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Container-title:Numerische Mathematik
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language:en
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Short-container-title:Numer. Math.
Abstract
AbstractIn this work we present a unified error analysis for abstract space discretizations of wave-type equations with nonlinear quasi-monotone operators. This yields an error bound in terms of discretization and interpolation errors that can be applied to various equations and space discretizations fitting in the abstract setting. We use the unified error analysis to prove novel convergence rates for a non-conforming finite element space discretization of wave equations with nonlinear acoustic boundary conditions and illustrate the error bound by a numerical experiment.
Funder
Karlsruher Institut für Technologie (KIT)
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics
Reference28 articles.
1. Arndt, D., Bangerth, W., Blais, B., Fehling, M., Gassmöller, R., Heister, T., Heltai, L., Köcher, U., Kronbichler, M., Maier, M., Munch, P., Pelteret, J.P., Proell, S., Simon, K., Turcksin, B., Wells, D., Zhang, J.: The deal.II library, version 9.3. J. Numer. Math. 28(3), 171–186 (2021) 2. Arndt, D., Bangerth, W., Davydov, D., Heister, T., Heltai, L., Kronbichler, M., Maier, M., Pelteret, J.P., Turcksin, B., Wells, D.: The deal.II finite element library: design, features, and insights. Comput. Math. Appl. 81, 407–422 (2021). https://doi.org/10.1016/j.camwa.2020.02.022 3. Springer Monographs in Mathematics;V Barbu,2010 4. Beale, J.T.: Spectral properties of an acoustic boundary condition. Indiana Univ. Math. J. 25(9), 895–917 (1976). https://doi.org/10.1512/iumj.1976.25.25071 5. Beale, J.T., Rosencrans, S.I.: Acoustic boundary conditions. Bull. Am. Math. Soc. 80, 1276–1278 (1974). https://doi.org/10.1090/S0002-9904-1974-13714-6
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