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W. Auzinger, O. Koch, A. Saboor Bagherzadeh:
"Error estimation based on locally weighted defect for boundary value problems in second order ordinary differential equations";
in: "ASC Report 29/2013", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2013, ISBN: 978-3-902627-06-3, 1 - 23.

We investigate e cient asymptotically correct a posteriori error
estimates for the numerical approximation of two-point boundary value problems for second order ordinary di erential equations by polynomial collocation methods. Our error indicators are based on the defect of the collocation solution with respect to an associated exact di erence scheme and backsolving using a cheap, low order nite-di erence scheme. We prove high asymptotical correctness of this error indicator and illustrate the theoretical analysis by numerical examples.

Second order boundary value problems Collocation methods Asymptotically correct a posteriori error estimates Defect correction principle Exact di erence scheme Supraconvergence

http://www.asc.tuwien.ac.at/preprint/2013/asc29x2013.pdf