| Abstract: |
| In this talk, we introduce and analyze a discontinuous Galerkin method for approximating the solutions of the stationary Boussinesq system, which models non-isothermal fluid flow. The model consists of incompressible Navier-Stokes equations, which describe the velocity and pressure of the fluid, coupled with an advection-diffusion equation for the temperature. We impose a Navier-type boundary condition on the velocity and a Dirichlet boundary condition on the temperature.
The proposed numerical scheme combines an interior penalty discontinuous Galerkin method with an upwind approach for the Boussinesq system. We prove existence and uniqueness results for the discrete scheme under a certain regularity assumption of the domain. A priori error estimates in terms of natural energy norms for the velocity, pressure, and temperature are also derived. We conclude with some numerical experiments. |
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