| Issue |
ESAIM: M2AN
Volume 58, Number 3, May-June 2024
|
|
|---|---|---|
| Page(s) | 881 - 926 | |
| DOI | https://doi.org/10.1051/m2an/2024017 | |
| Published online | 03 June 2024 | |
Unconditionally optimal error estimates of linearized Crank-Nicolson virtual element methods for quasilinear parabolic problems on general polygonal meshes
1
School of Mathematics and Statistics, Huangshi Key Laboratory of Metaverse and Virtual Simulation, Hubei Normal University, Huangshi 435002, P.R. China
2
School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, P.R. China
3
School of Mathematics and statistics, Lingnan Normal University, Zhanjiang, Guangdong 524048, P.R. China
* Corresponding author: liguanrong88@126.com
Received:
21
November
2023
Accepted:
8
March
2024
In this paper, we construct, analyze, and numerically validate a linearized Crank-Nicolson virtual element method (VEM) for solving quasilinear parabolic problems on general polygonal meshes. In particular, we consider the more general nonlinear term a(x, u), which does not require Lipschitz continuity or uniform ellipticity conditions. To ensure that the fully discrete solution remains bounded in L∞-norm, we construct two novel elliptic projections and apply a new error splitting technique. With the help of the boundedness of numerical solution and delicate analysis of the nonlinear term, we derive the optimal error estimates for any k-order VEMs without any time-step restrictions. Numerical experiments on various polygonal meshes validate the accuracy of theoretical analysis and the unconditional convergence of the proposed scheme.
Mathematics Subject Classification: 35K59 / 65M12 / 65M60
Key words: Error analysis / quasilinear parabolic problem / virtual element method / linearized Crank-Nicolson scheme
© The authors. Published by EDP Sciences, SMAI 2024
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