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

TL;DR

This paper introduces a method to generate bipartite meshes with controlled regularity for 2-D and 3-D domains, facilitating stable numerical solutions for physical problems.

Contribution

The paper presents a novel procedure for creating bipartite grids with prescribed size and regularity, applicable to simply connected domains in 2-D and 3-D.

Findings

Meshes have bounded regularity $oldsymbol{ ext{zeta}_K extless= C}$

Bipartite grids enable well-posed mixed variational formulations

Applicable to problems like porous media flow and linear phenomena

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 $\zeta_{K} \leq C$ where $\zeta_{K}$ 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.