Convergence estimates for essentially positive type discrete Dirichlet problems

Abstract

In this paper we consider a class of difference approximations to the Dirichlet problem for second-order elliptic operators with smooth coefficients. The main result is that if the order of accuracy of the approximate problem is V \mathcal {V} , and F F (the right-hand side) and f f (the boundary values) both belong to C λ {C^\lambda } for λ > V \lambda > \mathcal {V} , then the rate of convergence is O ( h λ ) O({h^\lambda }) .