# Finite element error analysis of wave equations with dynamic boundary conditions: L2 estimates

Hipp, David; Kovács, Balázs

Abstract:
$L^2$ error estimates of semi- and full discretisations of wave equations with dynamic boundary conditions are studied, using bulk–surface finite elements and Runge–Kutta methods. The analysis resides on an abstract formulation and error estimates, via energy techniques, within this abstract setting. Four prototypical linear wave equations with dynamic boundary conditions are analysed within the abstract framework. For problems with velocity terms, or with acoustic boundary conditions we prove a spatial convergence order which is less than two. These can also be observed in the presented numerical experiments.

 Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)Sonderforschungsbereich 1173 (SFB 1173) Publikationstyp Forschungsbericht Jahr 2018 Sprache Englisch Identifikator ISSN: 2365-662X URN: urn:nbn:de:swb:90-889318 KITopen-ID: 1000088931 Verlag KIT, Karlsruhe Umfang 40 S. Serie CRC 1173 ; 2018/53 Projektinformation SFB 1173/1 (DFG, DFG KOORD, SFB 1173/1 2015) Schlagworte wave equations, dynamic boundary conditions, abstract error analysis, Ritz map, $L^2$ error estimates, Runge–Kutta methods
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