Mathematical Modeling and Analysis Mimetic Discretizations of Diffusion Equation on

As mathematical modeling of uid ow be-comes more sophisticated, the need for discretiza-tion methods handling meshes with mixed types of elements is arisen. Practice experiences show that the most effec-tive discretization methods preserve and mimic the underlying properties of original continuum differential operators. Conservation laws, so-lution symmetries, and the fundamental identi-ties and theorems of vector and tensor calcu-lus are example of such properties. We devel-oped a new family of mimetic discretizations for diffusion-type equations (e.g. pressure equation in porous medium applications) on general polyg-onal meshes