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This paper is concerned with the mixed formulation of the Bous- sinesq equations in two-dimensional domains and its numerical approximation. The paper deals rst with existence and uniqueness results, as well as the description of the regularity of any solution. The problem is then approximated by a mixed nite element method, where the gradient of the velocity and the gradient of the temperature, quantities of practical importance, are introduced as new unknowns. An existence result for the nite element solution and convergence results are proved near a nonsingular solution. Quasi-optimal error estimates are nally presented.

A mixed formulation of Boussinesq equations: Analysis of nonsingular solutions