NSF grant DMS-1912779, NSF grant DMS-2208391
Mathematics of Computation
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
∆t ≤ Ch1+1/s , where ∆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.
This work is licensed under a Creative Commons Attribution 4.0 International License.
Locate the Document
Gopalakrishnan, Jay and Sun, Zheng, "Stability of Structure-Aware Taylor Methods for Tents" (2023). Mathematics and Statistics Faculty Publications and Presentations. 364.
First published in Mathematics of Computation in 92 2023, published by the American Mathematical Society