Mat-1.600 Laskennallisen tieteen ja
tekniikan seminaari
11.10.2004 klo
14.15
U356
Sergey
Korotov, Jyväskylän Yliopisto
A posteriori
error estimation in terms of linear functionals for the elliptic-type
boundary value problems
The talk is concerned with a posteriori error estimation in terms of
special problem-oriented quantities. In many practically interesting
cases, such a quantity is represented as a linear functional that
controls the behavior of a solution in certain subdomains, along some
lines, or at especially interesting points. The method of estimating
quantities of interest is usually based upon the analysis of the
adjoint boundary-value problem, whose right-hand side is formed by the
considered linear functional. On this way, we propose a new effective
modus operandi. It is based on two principles: (a) the original and
adjoint problems are solved on non-coinciding meshes, and (b) the term
presenting the product of gradients of errors of the primal and adjoint
problems is estimated by using the ``gradient averaging'' technique.
Numerical tests confirming the high effectivity of this approach will
be presented.