A refined mixed finite element method for the Boussinesq equations in polygonal domains (Q2725338)

This paper deals with the Boussinesq equations in two-dimensional polygonal domains and its numerical approximation. A mixed formulation with the original variables and the gradients of the velocity and the temperature is described, and elements of low degree are used. The steady solution has a singular behaviour near the corner points and it is shown to belong to appropriate weighted Sobolev spaces. Since uniform meshes lead to a slow convergence rate, appropriate refinement rules on the meshes near the corner points are designed to restore the quasi-optimal rate of convergence. A numerical test is finally presented which confirms the theoretical convergence rates.