Stability and error analysis of a new class of higher-order consistent splitting schemes for the Navier-Stokes equations
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909671967686656 |
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| author | Huang, Fukeng Shen, Jie |
| author_facet | Huang, Fukeng Shen, Jie |
| contents | A new class of fully decoupled consistent splitting schemes for the Navier-Stokes equations are constructed and analyzed in this paper. The schemes are based on the Taylor expansion at $t^{n+β}$ with $β\ge 1$ being a free parameter. It is shown that by choosing {\color{black} $β= 3, \,6,\,9$} respectively for the second-, third- and fourth-order schemes, their numerical solutions are uniformed bounded in a strong norm, and admit optimal global-in-time convergence rates in both 2D and 3D. {\color{black}These } results are the first stability and convergence results for any fully decoupled, higher than second-order schemes for the Navier-Stokes equations. Numerical results are provided to show that the third- and fourth-order schemes based on the usual BDF (i.e. $β=1$) are not unconditionally stable while the new third- and fourth-order schemes with suitable $β$ are unconditionally stable and lead to expected convergence rates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01296 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability and error analysis of a new class of higher-order consistent splitting schemes for the Navier-Stokes equations Huang, Fukeng Shen, Jie Numerical Analysis 65M12, 76D05, 65M15 A new class of fully decoupled consistent splitting schemes for the Navier-Stokes equations are constructed and analyzed in this paper. The schemes are based on the Taylor expansion at $t^{n+β}$ with $β\ge 1$ being a free parameter. It is shown that by choosing {\color{black} $β= 3, \,6,\,9$} respectively for the second-, third- and fourth-order schemes, their numerical solutions are uniformed bounded in a strong norm, and admit optimal global-in-time convergence rates in both 2D and 3D. {\color{black}These } results are the first stability and convergence results for any fully decoupled, higher than second-order schemes for the Navier-Stokes equations. Numerical results are provided to show that the third- and fourth-order schemes based on the usual BDF (i.e. $β=1$) are not unconditionally stable while the new third- and fourth-order schemes with suitable $β$ are unconditionally stable and lead to expected convergence rates. |
| title | Stability and error analysis of a new class of higher-order consistent splitting schemes for the Navier-Stokes equations |
| topic | Numerical Analysis 65M12, 76D05, 65M15 |
| url | https://arxiv.org/abs/2507.01296 |