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