Department of Mathematics, University of Bergen, Johannes Bruns Gate 12, 5008 Bergen, Norway
Copyright © 2009 Jan Valdman. This is an open access article distributed under the
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We consider a Poisson boundary value problem and its functional a posteriori error estimate derived by S. Repin in 1999. The estimate majorizes the seminorm of the error of the discrete solution computed by FEM method and contains a free ux variable from the (div) space. In order to keep the estimate sharp, a procedure for the minimization of the majorant term with respect to the ux variable is introduced, computing the free ux variable from a global linear system of equations. Since the linear system is symmetric and positive definite, few iterations of a conjugate gradient method with a geometrical multigrid preconditioner are applied. Numerical techniques are demonstated on one benchmark example with a smooth solution on a unit square domain including the computation of the approximate value of the constant in Friedrichs' inequality.