Avoiding slave points in an adaptive refinement procedure for convection-diffusion problems in 2D

A finite difference method is presented for singularly perturbed convection -diffusion problems with discretization error estimate of nearly second ord er. In a standard patched adaptive refinement method certain slave nodes ap pear where the approximation is done by interpolating the values of the app roximate solution at adjacent nodes. This deteriorates the accuracy of trun cation error. In order to avoid the slave points we change the stencil at t he interface points from a cross to a skew one. The efficiency of this tech nique is illustrated by numerical experiments in 2D.