Minimization of Functional Majorant in a Posteriori Error Analysis Based on H(div) Multigrid-Preconditioned CG Method. (12th July 2009)

• Record Type: Journal Article
• Authors: Valdman, Jan
• Other Names: Nicaise Serge Academic Editor.
• Is Part Of: Advances in numerical analysis. Volume 2009(2009)
• Publication Date: 2009-07-12
• Subjects: Numerical analysis -- Periodicals; Numerical analysis; Periodicals; Electronic journals; 518
• DOI: 10.1155/2009/164519
• Languages: English
• ISSNs: 1687-9562

Abstract

Abstract : We consider a Poisson boundary value problem and its functional a posteriori error estimate derived by S. Repin in 1999. The estimate majorizes theH 1 seminorm of the error of the discrete solution computed by FEM method and contains a free ux variable from theH (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.