Abstract
In this work we present and analyze a finite element scheme yielding discontinuous Galerkin approximations to the solutions of the stationary Boussinesq system for the simulation of non-isothermal flow phenomena. The model consists of a Navier–Stokes-type system, describing the velocity and the pressure of the fluid, coupled to an advection-diffusion equation for the temperature. The proposed numerical scheme is based on the standard interior penalty technique and an upwind approach for the nonlinear convective terms and employs the divergence-conforming Brezzi–Douglas–Marini (BDM) elements of order k for the velocity, discontinuous elements of order
Dedicated to the memory of Francisco-Javier Sayas
Funding statement: This research was partially supported by ANID-Chile through the pojects Fondecyt 11190241, Anillo of Computational Mathematics for Desalination Processes (ACT210087), and by Centro de Modelamiento Matemático (ACE210010 and FB210005); and by Universidad del Bío-Bío through VRIP-UBB project 2120173 GI/C.
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