W. Auzinger, H. Lehner, E. Weinmüller:

"An efficient asymptotically correct error estimator for collocation solutions to singular index-1 DAEs";

in: "ASC Report 18/2010", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2010, ISBN: 978-3-902627-03-2.

A computationally efficient a posteriori error estimator is

introduced and analyzed for collocation solutions to linear

index-1 differential-algebraic equations with properly stated

leading term exhibiting a singularity of the first kind. The

procedure is based on a modified defect correction principle,

extending an established technique from the context of ordinary differential

equations to the differential-algebraic case.

Using recent convergence results for collocation methods, we prove

that the resulting error estimate is asymptotically correct.

Numerical examples demonstrate the performance of this approach.

To keep the presentation reasonably self-contained, some

arguments from the literature on differential-algebraic equations

concerning the decoupling of the problem and its discretization,

which is essential for our analysis, are also briefly reviewed.

The appendix contains a remark about the interrelation between

collocation and implicit Runge-Kutta methods for

differential-algebraic equations.

Differential algebraic equations ¢ singularity of the first kind ¢ collocation ¢ a posteriori error estimation ¢ defect correction

http://www.asc.tuwien.ac.at/preprint/2010/asc18x2010.pdf

Created from the Publication Database of the Vienna University of Technology.