We present a procedure to generate bipartite grids for simply connected domains in 2-D and 3-D of prescribed size and controlled regularity elements. The mesh elements K of the triangulation satisfy ?K ? C where ?K is the regularity and C is a constant depending on the shape parameters of the initial mesh. Bipartite grids permit a well-posed mixed-mixed variational formulation of problems such as the porous media flow equation and other linear physical phenomena as well as Galerkin-type discontinuous relaxations.