Refined mixed finite element method for the Boussinesq equations in polygonal domains

This paper deals with the mixed formulation of the Boussinesq equations in two-dimensional polygonal domains and its numerical approximation. The solu tions have a singular behaviour near the non-convex; corner points so that we show that they belong to appropriate weighted Sobolev spaces. We further derive appropriate refinement rules on the meshes near the corner points i n order to restore the quasi-optimal rate of convergence. (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.