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

@article{Veiga2022AFV,
  title={A fully-discrete virtual element method for the nonstationary Boussinesq equations},
  author={Lourencco Beirao da Veiga and David Mora and Alberth Silgado},
  journal={ArXiv},
  year={2022},
  volume={abs/2209.12311}
}
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… 

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References

SHOWING 1-10 OF 59 REFERENCES

A Mixed Virtual Element Method for The Boussinesq Problem on Polygonal meshes

This work uses a mixed virtual element method (mixed-VEM) for the two-dimensional stationary Boussinesq problem in such a way that the pseudostress and the velocity are approximated on virtual element subspaces of H(div) and H, respectively, whereas a VEM is proposed to approximate the temperature.

An exactly divergence-free finite element method for a generalized Boussinesq problem

A mixed finite element method with exactly divergence-free velocities for the numerical simulation of a generalized Boussinesq problem, describing the motion of a nonisothermal incompressible fluid subject to a heat source is proposed and analysed.

A virtual element discretization for the time dependent Navier-Stokes equations in stream-function formulation

A new Virtual Element Method of arbitrary order for the time dependent Navier-Stokes equations in stream-function form is proposed and analyzed, and error estimations are derived and shown that the method is optimally convergent in both space and time variables.

On the finite element approximation of the nonstationary Navier-Stokes problem

In this note we report some basic convergence results for the semi-discrete finite element Galerkin approximation of the nonstationary Navier-Stokes problem. Asymptotic error estimates are

Stabilized Finite Element Methods for the Oberbeck–Boussinesq Model

Conforming finite element approximations for the time-dependent Oberbeck–Boussinesq model with inf-sup stable pairs for velocity and pressure are considered with a stabilization of the incompressibility constraint and a stability and convergence analysis is given.

Analysis of a fourth order finite difference method for the incompressible Boussinesq equations

Summary.The convergence of a fourth order finite difference method for the 2-D unsteady, viscous incompressible Boussinesq equations, based on the vorticity-stream function formulation, is

A mixed virtual element method for the Brinkman problem

This paper introduces and analyzes a mixed virtual element method (mixed-VEM) for the two-dimensional Brinkman model of porous media flow with non-homogeneous Dirichlet boundary conditions, in which the only unknown is given by the pseudostress, whereas the velocity and pressure are computed via postprocessing formulae.

A Stream Virtual Element Formulation of the Stokes Problem on Polygonal Meshes

A novel stream formulation of the virtual element method (VEM) for the solution of the Stokes problem is proposed and analyzed and it is equivalent to the velocity-pressure (inf-sup stable) mimetic scheme presented.
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