Volume 57, Number 3, May-June 2023
|Page(s)||1143 - 1170|
|Published online||08 May 2023|
A variable time-step IMEX-BDF2 SAV scheme and its sharp error estimate for the Navier–Stokes equations
Research Center for Mathematics, Beijing Normal University, Zhuhai 519087, P.R. China
2 Department of Mathematical Sciences, BNU-HKBU United International College, Zhuhai 519087, China
3 School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P.R. China
4 School of Mathematical Science, Xiamen University, Xiamen 361005, China
5 Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA
6 School of Mathematics and Statistics, Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan 430072, P.R. China
* Corresponding author: firstname.lastname@example.org
Accepted: 22 January 2023
We generalize the implicit-explicit (IMEX) second-order backward difference (BDF2) scalar auxiliary variable (SAV) scheme for Navier–Stokes equation with periodic boundary conditions (Huang and Shen, SIAM J. Numer. Anal. 59 (2021) 2926–2954) to a variable time-step IMEX-BDF2 SAV scheme, and carry out a rigorous stability and convergence analysis. The key ingredients of our analysis are a new modified discrete Grönwall inequality, exploration of the discrete orthogonal convolution (DOC) kernels, and the unconditional stability of the proposed scheme. We derive global and local optimal H1 error estimates in 2D and 3D, respectively. Our analysis provides a theoretical support for solving Navier–Stokes equations using variable time-step IMEX-BDF2 SAV schemes. We also design an adaptive time-stepping strategy, and provide ample numerical examples to confirm the effectiveness and efficiency of our proposed methods.
Mathematics Subject Classification: 65M15 / 76D05 / 65M70
Key words: Navier–Stokes / variable time stepping / error analysis
Note to the reader: Affiliation 4 has been installed for all authors instead of indicating it only to author Jie Shen. Authors' affiliations has been corrected on 18 May 2023.
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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