R. Vanselow et Hp. Scheffler, CONVERGENCE ANALYSIS OF A FINITE-VOLUME METHOD VIA A NEW NONCONFORMING FINITE-ELEMENT METHOD, Numerical methods for partial differential equations, 14(2), 1998, pp. 213-231
The article is devoted to the study of convergence properties of a Fin
ite Volume Method (FVM) using Voronoi boxes for discretization. The ap
proach is based on the construction of a new nonconforming Finite Elem
ent Method (FEM), such that the system of linear equations coincides c
ompletely with that for the FVM. Thus, by proving convergence properti
es of the FEM, we obtain similar ones of the FVM. In this article, the
investigations are restricted to the Poisson equation. (C) 1998 John
Wiley gr Sons, Inc.