A fully-discrete virtual element method for the nonstationary Boussinesq equations
Numerical Analysis
2023-03-22 v1 Numerical Analysis
Abstract
In the present work we propose and analyze a fully coupled virtual element method of high order for solving the two dimensional nonstationary Boussinesq system in terms of the stream-function and temperature fields. The discretization for the spatial variables is based on the coupling - and -conforming virtual element approaches, while a backward Euler scheme is employed for the temporal variable. Well-posedness and unconditional stability of the fully-discrete problem is provided. Moreover, error estimates in - and -norms are derived for the stream-function and temperature, respectively. Finally, a set of benchmark tests are reported to confirm the theoretical error bounds and illustrate the behavior of the fully-discrete scheme.
Cite
@article{arxiv.2209.12311,
title = {A fully-discrete virtual element method for the nonstationary Boussinesq equations},
author = {L. Beirão da Veiga and D. Mora and A. Silgado},
journal= {arXiv preprint arXiv:2209.12311},
year = {2023}
}