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• W4295693432 abstract "In this paper, we analyze the first-order implicit-explicit type scheme based on the scalar auxiliary variable (SAV) with divergence-free <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper H Superscript 1> <mml:semantics> <mml:msup> <mml:mi>H</mml:mi> <mml:mn>1</mml:mn> </mml:msup> <mml:annotation encoding=application/x-tex>H^1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> conforming finite element method (FEM) in space for the evolutionary incompressible Navier-Stokes equations at high Reynolds number. The stability and a priori error estimates are given, in which the constants are independent of the Reynolds number. The velocity energy estimate is given without any condition on the time step, however, the a priori error estimates for the velocity are obtained with severe time step restrictions. In addition, a Reynolds-dependent error bound with convergence order of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=k plus 1> <mml:semantics> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>k+1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> in space is also obtained for the velocity error in the <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper L squared> <mml:semantics> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:annotation encoding=application/x-tex>L^2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> norm with no time step restrictions. Here, <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=k> <mml:semantics> <mml:mi>k</mml:mi> <mml:annotation encoding=application/x-tex>k</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is the polynomial order of the velocity space. Some numerical experiments are carried out to verify the analytical results." @default.
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• W4295693432 date "2022-10-13" @default.
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• W4295693432 title "Analysis of divergence-free 𝐻¹ conforming FEM with IMEX-SAV scheme for the Navier-Stokes equations at high Reynolds number" @default.
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• W4295693432 doi "https://doi.org/10.1090/mcom/3790" @default.
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