A mixed formulation of Boussinesq equations: Analysis of nonsingular solutions

This paper is concerned with the mixed formulation of the Boussinesq equati ons in two-dimensional domains and its numerical approximation. The paper d eals first with existence and uniqueness results, as well as the descriptio n of the regularity of any solution. The problem is then approximated by a mixed finite element method, where the gradient Of the velocity and the gra dient of the temperature, quantities of practical importance, are introduce d as new unknowns. An existence result for the finite element solution and convergence results are proved near a nonsingular solution. Quasi-optimal e rror estimates are finally presented.