Error Analysis of the Finite-Volume Method with Respect to Mesh Type

This article presents truncation error terms for flux approximations on mesh faces, needed by the finite-volume method, and their influence on solution accuracy in the search for the optimal cell type. Face truncation errors are used to assemble truncation errors for different cell types such as squares, triangles, and hexagons. It is shown that squares have the smallest and triangles the largest truncation errors, for the same cell size, which is also confirmed by numerical experiments. It is also shown that polyhedral meshes consisting of hexagons are slightly less accurate than hexahedral meshes with the same cell size.