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Unified error analysis for non-conforming space discretizations ofwave-type equations

Hipp, David; Hochbruck, Marlis; Stohrer, Christian


This paper provides a unified error analysis for non-conforming space discretizations of linear wave equations in time-domain. We propose a framework which studies wave equations as first-order evolution equations in Hilbert spaces and their space discretizations as differential equations in finite dimensional Hilbert spaces. A lift operator maps the semi-discrete solution from the approximation space to the continuous space. Our main results are a priori error bounds in terms of interpolation, data and conformity errors of the method. Such error bounds are the key to the systematic derivation of convergence rates for a large class of problems. To show that this approach significantly eases the proof of new convergence rates, we apply it to an isoparametric finite element discretization of the wave equation with acoustic boundary conditions in a smooth domain. Moreover, our results reproduce known convergence rates for already investigated conforming and non-conforming space discretizations in a concise and unified way. The examples discussed in this paper comprise discontinuous Galerkin discretizations of Maxwell’s equations and finite elements with mass lumping for the acoustic wave equation.

Volltext §
DOI: 10.5445/IR/1000076637
Veröffentlicht am 16.11.2017
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2017
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000076637
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 36 S.
Serie CRC 1173 ; 2017/29
Schlagwörter wave equation, non-conforming space discretization, abstract error analysis, a priori error bounds, linear evolution equations, operator semigroups, linear monotone operators in Hilbert spaces, dynamic boundary conditions, isoparametric finite elements
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