Stability of structure-aware Taylor methods for tents
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- by Jay Gopalakrishnan and Zheng Sun;
- Math. Comp. 92 (2023), 1061-1086
- DOI: https://doi.org/10.1090/mcom/3811
- Published electronically: January 27, 2023
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Abstract:
Structure-aware Taylor (SAT) methods are a class of timestepping schemes designed for propagating linear hyperbolic solutions within a tent-shaped spacetime region. Tents are useful to design explicit time marching schemes on unstructured advancing fronts with built-in locally variable timestepping for arbitrary spatial and temporal discretization orders. The main result of this paper is that an $s$-stage SAT timestepping within a tent is weakly stable under the time step constraint $\Delta t \leq Ch^{1+1/s}$, where $\Delta t$ is the time step size and $h$ is the spatial mesh size. Improved stability properties are also presented for high-order SAT time discretizations coupled with low-order spatial polynomials. A numerical verification of the sharpness of proven estimates is also included.References
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Bibliographic Information
- Jay Gopalakrishnan
- Affiliation: Fariborz Maseeh Department of Mathematics and Statistics, Portland State University, P.O. Box 751, Portland, Oregon 97207
- MR Author ID: 661361
- ORCID: 0000-0001-7508-3232
- Email: gjay@pdx.edu
- Zheng Sun
- Affiliation: Department of Mathematics, The University of Alabama, Box 870350, Tuscaloosa, Alabama 35487
- ORCID: 0000-0003-3763-3015
- Email: zsun30@ua.edu
- Received by editor(s): March 9, 2022
- Received by editor(s) in revised form: October 13, 2022
- Published electronically: January 27, 2023
- Additional Notes: The work of the first author was partially supported by the NSF grant DMS-1912779. The work of the second author was partially supported by the NSF grant DMS-2208391.
The second author is the corresponding author. - © Copyright 2023 American Mathematical Society
- Journal: Math. Comp. 92 (2023), 1061-1086
- MSC (2020): Primary 65M12
- DOI: https://doi.org/10.1090/mcom/3811
- MathSciNet review: 4550320