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Full discretization error analysis of exponential integrators for semilinear wave equations

Dörich, Benjamin ORCID iD icon; Leibold, Jan


In this article we prove full discretization error bounds for semilinear second-order evolution equations. We consider exponential integrators in time applied to an abstract nonconforming semi discretization in space. Since the fully discrete schemes involve the spatially discretized semigroup, a crucial point in the error analysis is to eliminate the continuous semigroup in the representation of the exact solution. Hence, we derive a modified variation-of-constants formula driven by the spatially discretized semigroup which holds up to a discretization error. Our main results provide bounds for the full discretization errors for exponential Adams and explicit exponential Runge–Kutta methods. We show convergence with the stiff order of the corresponding exponential integrator in time, and errors stemming from the spatial discretization.
As an application of the abstract theory, we consider an acoustic wave equation with kinetic boundary conditions, for which we also present some numerical experiments to illustrate our results.

Volltext §
DOI: 10.5445/IR/1000135100
Veröffentlicht am 07.07.2021
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsmonat/-jahr 07.2021
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000135100
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 22 S.
Serie CRC 1173 Preprint ; 2021/31
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter error analysis, full discretization, exponential integrators, wave equation, semilinear evolution equations, dynamic boundary conditions, conconforming space discretization, a-priori error bounds
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