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Contributions to Proceedings:

W. Auzinger:
"Error estimation techniques based on defect computation and global reconstruction";
in: "International Conference on Numerical Analysis and Applied Mathematics", issued by: American Institute of Physics; American Institute of Physics, 2010, ISBN: 978-0-7354-0831-9, 4 pages.



English abstract:
The well-known technique of defect correction has been used in various moldings for numerical integration of
differential or integral equations. Essentially, it can be traced back to the work of P.E.Zadunaiskky where the idea was presented in in the context of initial value problems for ODEs, and H.J.Stetter, where a general discussion of the principle is given. Here we focus on use of this principle as a tool in estimating local or global errors in a reliable and efficient way. Our general setting and guiding principle
is presented in Section 2. In Section we first consider boundary value problems for ODEs. Since the main purpose of an error
estimate is mesh adaptation, an essential requirement is that it has to be robust with respect to arbitrarily distributed mesh
points, and we will exemplify how this can be achieved. In particular, we consider explicit first and second order problems.
We sketch the idea how to argue asymptotic correctness and present a numerical example. We also propose a related approach
for estimating the error of a splitting scheme for evolution equations. Some remarks on elliptic PDEs are given in Section 3.

Keywords:
error estimation, defect correctio, splitting methods

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