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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";
BIT Numerical Mathematics, 54 (2014), 4; S. 873 - 900.

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.

http://dx.doi.org/10.1007/s10543-014-0488-y

http://link.springer.com/article/10.1007/s10543-014-0488-y