Trigonometric integrators for quasilinear wave equations
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- by Ludwig Gauckler, Jianfeng Lu, Jeremy L. Marzuola, Frédéric Rousset and Katharina Schratz HTML | PDF
- Math. Comp. 88 (2019), 717-749 Request permission
Abstract:
Trigonometric time integrators are introduced as a class of explicit numerical methods for quasilinear wave equations. Second-order convergence for the semidiscretization in time with these integrators is shown for a sufficiently regular exact solution. The time integrators are also combined with a Fourier spectral method into a fully discrete scheme, for which error bounds are provided without requiring any CFL-type coupling of the discretization parameters. The proofs of the error bounds are based on energy techniques and on the semiclassical Gårding inequality.References
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Additional Information
- Ludwig Gauckler
- Affiliation: Institut für Mathematik, Freie Universität Berlin, Arnimallee 9, D-14195 Berlin, Germany
- MR Author ID: 832307
- Email: gauckler@math.fu-berlin.de
- Jianfeng Lu
- Affiliation: Departments of Mathematics, Physics, and Chemistry, Duke University, Box 90320, Durham, North Carolina 27708
- MR Author ID: 822782
- ORCID: 0000-0001-6255-5165
- Email: jianfeng@math.duke.edu
- Jeremy L. Marzuola
- Affiliation: Department of Mathematics, UNC-Chapel Hill, CB#3250 Phillips Hall, Chapel Hill, North Carolina 27599
- MR Author ID: 787291
- Email: marzuola@math.unc.edu
- Frédéric Rousset
- Affiliation: Laboratoire de Mathématiques d’Orsay (UMR 8628), Université Paris-Sud, 91405 Orsay Cedex, France; and Institut Universitaire de France
- Email: frederic.rousset@math.u-psud.fr
- Katharina Schratz
- Affiliation: Fakultät für Mathematik, Karlsruhe Institute of Technology, Englerstr. 2, D-76131 Karlsruhe, Germany
- MR Author ID: 990639
- Email: katharina.schratz@kit.edu
- Received by editor(s): February 9, 2017
- Received by editor(s) in revised form: August 25, 2017, and November 3, 2017
- Published electronically: May 4, 2018
- Additional Notes: This work was supported by Deutsche Forschungsgemeinschaft (DFG) through project GA 2073/2-1 (LG), SFB 1114 (LG) and SFB 1173 (KS) and by National Science Foundation (NSF) under grants DMS-1454939 (JL), DMS-1312874 (JLM) and DMS-1352353 (JLM)
- © Copyright 2018 American Mathematical Society
- Journal: Math. Comp. 88 (2019), 717-749
- MSC (2010): Primary 65M15; Secondary 65P10, 65L70, 65M20
- DOI: https://doi.org/10.1090/mcom/3339
- MathSciNet review: 3882282