A fully-discrete virtual element method for the nonstationary Boussinesq equations

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 $C^1$- and $C^0$-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 $H^2$- and $H^1$-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.

References in corpus (3)

• Pressure-robust analysis of divergence-free and conforming FEM for evolutionary incompressible Navier-Stokes flows
• Optimal error estimates of coupled and divergence-free virtual element methods for the Poisson--Nernst--Planck/Navier--Stokes equations
• Some Estimates of Virtual Element Methods for Fourth Order Problems