On the generation of bipartite grids with controlled regularity for 2-D and 3-D simply connected domains

Abstract

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 $ζ_{K} \leq C$ where $ζ_{K}$ 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.