Stability of structure-aware Taylor methods for tents

03/10/2022

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by   Jay Gopalakrishnan, et al.

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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 Δ t ≤ Ch^1+1/s, where Δ 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.