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Mathematics of Computation

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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

∆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.


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First published in Mathematics of Computation in 92 2023, published by the American Mathematical Society

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