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A unified error analysis for spatial discretizations of wave-type equations with applications to dynamic boundary conditions

Hipp, David

Abstract:
This thesis provides a unified framework for the error analysis of non-conforming space discretizations of linear wave equations in time-domain, which can be cast as symmetric hyperbolic systems or second-order wave equations. Such problems can be written as first-order evolution equations in Hilbert spaces with linear monotone operators. We employ semigroup theory for the well-posedness analysis and to obtain stability estimates for the space discretizations. To compare the finite dimensional approximations with the original solution, we use the concept of a lift from the discrete to the continuous space. Time integration with the Crank–Nicolson method is analyzed. In this framework, we derive a priori error bounds for the abstract space semi-discretization in terms of interpolation and discretization errors. These error bounds yield previously unkown convergence rates for isoparametric finite element discretizations of wave equations with dynamic boundary conditions in smooth domains. Moreover, our results allow to consider already investigated space discretizations in a unified way. Here it successfully reproduces known error bou ... mehr


Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Hochschulschrift
Jahr 2017
Sprache Englisch
Identifikator DOI(KIT): 10.5445/IR/1000070952
URN: urn:nbn:de:swb:90-709525
KITopen ID: 1000070952
Verlag Karlsruhe
Umfang XVI, 105 S.
Abschlussart Dissertation
Fakultät Fakultät für Mathematik (MATH)
Institut Institut für Angewandte und Numerische Mathematik (IANM)
Prüfungsdatum 14.06.2017
Referent/Betreuer Prof. M. Hochbruck
Projektinformation SFB 1173/1 (DFG, DFG KOORD, SFB 1173/1 2015)
Schlagworte Numerical analysis of linear evolution equations; Operator semigroups; Linear monotone operators in Gelfand triples of Hilbert spaces; Variational formulation; Wave equations; Abstract error analysis; A priori error bounds; Convergence rates; Non-conforming space discretization; boundary conditions; dynamic boundary conditions;
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