W. Auzinger, O. Koch, E. Weinmüller:
"Efficient Collocation Schemes for Singular Boundary Value Problems";
Numerical Algorithms, 31 (2002), S. 5 - 25.

Kurzfassung englisch:
We discuss an error estimation procedure for the global error of collocation schemes applied to solve singular boundary value problems with a singularity of the first kind. This estimate of the global error was proposed by Stetter in 1978 and is based on the idea of Defect Correction, originally due to Zadunaisky. A carefully designed modification of this estimate presented here, not only results in less computational work but also proves robust with respect to the singularity. This estimate also provides a basis for a grid selection routine in which the grid is modified with the aim to equidistribute the global error. This procedure yields meshes suitable for an efficient numerical solution - most importantly, we observe that the grid is refined in a way reflecting only the behavior of the solution and remains unaffected by the unsmooth direction field close to the singular point.

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