Analysis of divergence-free 𝐻¹ conforming FEM with IMEX-SAV scheme for the Navier-Stokes equations at high Reynolds number
| Autor: | Yongbin Han, Yanren Hou, Min Zhang |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Mathematics of Computation. 92:557-582 |
| ISSN: | 1088-6842 0025-5718 |
| DOI: | 10.1090/mcom/3790 |
| Popis: | In this paper, we analyze the first-order implicit-explicit type scheme based on the scalar auxiliary variable (SAV) with divergence-free H 1 H^1 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 k + 1 k+1 in space is also obtained for the velocity error in the L 2 L^2 norm with no time step restrictions. Here, k k is the polynomial order of the velocity space. Some numerical experiments are carried out to verify the analytical results. |
| Databáze: | OpenAIRE |
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