Exact integration formulas for the finite volume element method on simplicial meshes. Numerical Methods for Partial Differential Equations

This article considers the technological aspects of the finite volume element method for the numerical solu-tion of partial differential equations on simplicial grids in two and three dimensions. We derive new classes of integration formulas for the exact integration of generic monomials of barycentric coordinates over dif-ferent types of fundamental shapes corresponding to a barycentric dual mesh. These integration formulas constitute an essential component for the development of high-order accurate finite volume element schemes. Numerical examples are presented that illustrate the validity of the technology. © 2007 Wiley Periodicals