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.