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• W4311432812 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 <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=s> <mml:semantics> <mml:mi>s</mml:mi> <mml:annotation encoding=application/x-tex>s</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-stage SAT timestepping within a tent is weakly stable under the time step constraint <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=normal upper Delta t less-than-or-equal-to upper C h Superscript 1 plus 1 slash s> <mml:semantics> <mml:mrow> <mml:mi mathvariant=normal>Δ<!-- Δ --></mml:mi> <mml:mi>t</mml:mi> <mml:mo>≤<!-- ≤ --></mml:mo> <mml:mi>C</mml:mi> <mml:msup> <mml:mi>h</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>s</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> <mml:annotation encoding=application/x-tex>Delta t leq Ch^{1+1/s}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, where <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=normal upper Delta t> <mml:semantics> <mml:mrow> <mml:mi mathvariant=normal>Δ<!-- Δ --></mml:mi> <mml:mi>t</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>Delta t</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is the time step size and <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=h> <mml:semantics> <mml:mi>h</mml:mi> <mml:annotation encoding=application/x-tex>h</mml:annotation> </mml:semantics> </mml:math> </inline-formula> 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." @default.
• W4311432812 created "2022-12-26" @default.
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• W4311432812 date "2023-01-27" @default.
• W4311432812 modified "2023-10-11" @default.
• W4311432812 title "Stability of structure-aware Taylor methods for tents" @default.
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• W4311432812 doi "https://doi.org/10.1090/mcom/3811" @default.
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