[Back]

W. Auzinger, H. Lehner, E. Weinmüller:
"Defect-based a posteriori error estimation for index-1 DAEs";
in: "ASC Report 20/2007", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2007, ISBN: 978-3-902627-00-1.

A computationally efficient a posteriori error estimator is introduced and analyzed for collocation
solutions to linear index-1 DAEs with properly stated leading term. The procedure is based on a modified
defect correction principle, extending an established technique from the ODE context to the DAE case.
We prove that the resulting error estimate is asymptotically correct, and illustrate the method by means
of a numerical example.
To keep the presentation reasonably self-contained, we also briefly review some arguments from the
literature on DAEs concerning the decoupling of the problem and its discretization, which is essential for
our analysis.

Differential algebraic equations; collocation; a posteriori error estimation; defect correction

http://www.asc.tuwien.ac.at/preprint/2007/asc20x2007.pdf