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Zeitschriftenartikel:

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.


"Offizielle" elektronische Version der Publikation (entsprechend ihrem Digital Object Identifier - DOI)
http://dx.doi.org/10.1023/A:1021151821275

Elektronische Version der Publikation:
http://www.math.tuwien.ac.at/~ewa/PDF_Files/ecs_published.pdf


Erstellt aus der Publikationsdatenbank der Technischen Universitšt Wien.