Defect Correction for the Solution of a Singular Perturbation Problem

摘要

A method is described for the accurate discretization of a differential equation in which the highest derivative is multiplied by a small parameter. It is well known that for such singular perturbation problems with a strongly asymmetric differential operator almost all discretizations are either unstable or inaccurate or direction dependent. By the combination, in an iterative process, of an inaccurate stable and an accurate unstable scheme we obtain an accurate stable solution, without adapting the scheme to the flow direction. Two approximate solutions are obtained that are both accurate in the smooth part of the solution. The difference between both solutions can be used for the detection of the unsmooth parts.