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Minimization of Functional Majorant in a Posteriori Error Analysis Based on H(div) Multigrid-Preconditioned CG Method
Author
Source
Advances in Numerical Analysis
Issue
Vol. 2009, Issue 2009 (31 Dec. 2009), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2009-07-12
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
We consider a Poisson boundary value problem and its functional a posteriori error estimate derived by S.
Repin in 1999.
The estimate majorizes the H1 seminorm of the error of the discrete solution computed by FEM method and contains a free ux variable from the H(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.
American Psychological Association (APA)
Valdman, Jan. 2009. Minimization of Functional Majorant in a Posteriori Error Analysis Based on H(div) Multigrid-Preconditioned CG Method. Advances in Numerical Analysis،Vol. 2009, no. 2009, pp.1-15.
https://search.emarefa.net/detail/BIM-451018
Modern Language Association (MLA)
Valdman, Jan. Minimization of Functional Majorant in a Posteriori Error Analysis Based on H(div) Multigrid-Preconditioned CG Method. Advances in Numerical Analysis No. 2009 (2009), pp.1-15.
https://search.emarefa.net/detail/BIM-451018
American Medical Association (AMA)
Valdman, Jan. Minimization of Functional Majorant in a Posteriori Error Analysis Based on H(div) Multigrid-Preconditioned CG Method. Advances in Numerical Analysis. 2009. Vol. 2009, no. 2009, pp.1-15.
https://search.emarefa.net/detail/BIM-451018
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-451018