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Abstract The paper presents a defect correction method to solve singularly perturbed problems with discontinuous coefficient and point source. The method combines an inexpensive, lower-order stable, upwind difference scheme and a higher-order, less stable central difference scheme over a layer-adapted mesh. The mesh is designed so that most mesh points remain in the regions with rapid transitions. A posteriori error analysis is presented. The proposed numerical method is analyzed for consistency, stability, and convergence. The error estimates of the proposed numerical method satisfy parameter-uniform second-order convergence on the layer-adapted grid. The convergence obtained is optimal because it is free from any logarithmic term. The numerical analysis confirms the theoretical error analysis.
Kaushik et al. (Fri,) studied this question.