| Issue |
ESAIM: M2AN
Volume 56, Number 6, November-December 2022
|
|
|---|---|---|
| Page(s) | 2105 - 2139 | |
| DOI | https://doi.org/10.1051/m2an/2022073 | |
| Published online | 03 November 2022 | |
Analysis of fully discrete finite element methods for 2D Navier–Stokes equations with critical initial data
1
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong
2
Graduate School of Mathematical Science, The University of Tokyo, Tokyo, Japan
* Corresponding author: maisie.ma@connect.polyu.hk
Received:
19
June
2021
Accepted:
5
August
2022
First-order convergence in time and space is proved for a fully discrete semi-implicit finite element method for the two-dimensional Navier–Stokes equations with L2 initial data in convex polygonal domains, without extra regularity assumptions or grid-ratio conditions. The proof utilises the smoothing properties of the Navier–Stokes equations in the analysis of the consistency errors, an appropriate duality argument, and the smallness of the numerical solution in the discrete L2(0, tm; H1) norm when tm is smaller than some constant. Numerical examples are provided to support the theoretical analysis.
Mathematics Subject Classification: 65M12 / 65M15 / 76D05
Key words: Navier–Stokes equations / L2 initial data / semi-implicit Euler scheme / finite element method / error estimate
© The authors. Published by EDP Sciences, SMAI 2022
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