Mat-1.3656 Numeerisen analyysin ja laskennallisen tieteen seminaari.


Ma 26.11. 2007 klo 14.15

Olli Mali, Jyväskylän Yliopisto

Error control for problems with uncertain data by functional a posteriori estimates

First the functional a posteriori error estimators introduced by book [1] (minorant and majorant) are derived for elliptic boundary value problem via non-variational method. The relationship between functional error estimators and other methods are discussed.

The influence of errors arising due to indeterminacy in the problem data is investigated. Analysis is based on the functional a posteriori estimates discussed earlier. These estimates can be used to produce guaranteed and computable upper bounds for worst and best case error arising from indeterminant input data. As an example, bounds are derived for Poisson equation with indeterminant operator. We shortly present the numerical tools required for computation of bounds.

In practical engineering applications indeterminacy is constantly present but has been often neglected in simulations due to it's complicated nature. Reducing numerical approximation error without considering the effect of indeterminacy doesn't improve the reliability of simulation. Numerical tests are performed to demonstrate this.

Keywords: Indeterminacy, uncertainty, functional error estimate, majorant, error estimate, reliability

References:

[1] P. Neittaanmäki and Sergey Repin:
Reliable Methods for Computer Simulation, Error Control and A Posteriori
Estimates, Elsevier 2004