Abstract
A finite difference method is presented for singularly perturbed convection-diffusion problems with discretization error estimate of nearly second order. In a standard patched adaptive refinement method certain slave nodes appear where the approximation is done by interpolating the values of the approximate solution at adjacent nodes. This deteriorates the accuracy of truncation error. In order to avoid the slave points we change the stencil at the interface points from a cross to a skew one. The efficiency of this technique is illustrated by numerical experiments in 2D.
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Axelsson, O., Nikolova, M. Avoiding slave points in an adaptive refinement procedure for convection-diffusion problems in 2D. Computing 61, 331–357 (1998). https://doi.org/10.1007/BF02684384
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DOI: https://doi.org/10.1007/BF02684384