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W. Auzinger, A. Saboor Bagherzadeh, O. Koch:
"A posteriori error estimation for second order ODEs via defect integration";
Vortrag: 5th Austrian Numerical Analysis Day, Innsbruck; 07.05.2009 - 08.05.2009.

We discuss an estimation procedure for the global error of piecewise polynomial collocation for the solution of two-point boundary value problems for second order ODEs. This estimate is based on a defect correction principle. It is realized by solving an auxiliary, low order scheme including an appropriately weighted defect constructed via local quadrature means of the pointwise defect. The method is designed in a way directly applicable to the second order formulation, automatically taking account of the jumps (the smoothness defect') in the second derivative of the collocation function. The a posteriori estimate is proven to be asymptotically correct, and this proposition is illustrated by numerical examples.