Publications in Scientific Journals:
W. Auzinger, O. Koch, E. Weinmüller:
"Efficient Collocation Schemes for Singular Boundary Value Problems";
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.
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.