  In this article, we improve the convergence order of some finite volume
solutions approximating some second order elliptic problems. We prove that
finite volume approximations of order $O(h^{k+1})$, with $k$ integer, can be
obtained after $k$ corrections, starting with finite volume solution of order
$O(h)$, by using the same matrix and changing only the second member of the
original system. This is done for general smooth second order elliptic problems
in one dimension and for second order elliptic problems of the form $-\Delta
u+pu=f$, with Dirichlet conditions. Numerical tests justifying theoretical
results and showing the efficiency of the method are presented. The idea used
behind these results is the one of Fox's difference correction in the context
of finite difference method.
