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Monotonicity recovering and accuracy preserving optimization methods for postprocessing finite element solutions
Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.ORCID iD: 0000-0003-1836-4200
Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russia.
Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russia.
2011 (English)Report (Other academic)
Abstract [en]

We suggest here a least-change correction to available finite element (FE) solution.This postprocessing procedure is aimed at recoveringthe monotonicity and some other important properties that may not beexhibited by the FE solution. It is based on solvinga monotonic regression problem with some extra constraints.One of them is a linear equality-type constraint which models the conservativityrequirement. The other ones are box-type constraints, andthey originate from the discrete maximum principle.The resulting postprocessing problem is a large scale quadratic optimization problem. It is proved that the postprocessedFE solution preserves the accuracy of the discrete FE approximation.We introduce an algorithm for solving the postprocessingproblem. It can be viewed as a dual ascent method basedon the Lagrangian relaxation of the equality constraint.We justify theoretically its correctness.Its efficiency is demonstrated by the presented results of numerical experiments.

Place, publisher, year, edition, pages
Linköping: Linköping University, Electronic Press , 2011. , 28 p.
LiTH-MAT-R, ISSN 0348-2960 ; 8
Keyword [en]
Constrained monotonic regression, Large scale quadratic optimization, Lagrangian relaxation, Dual ascent method, Finite element solution, Accuracy analysis
National Category
Computational Mathematics Computational Mathematics
URN: urn:nbn:se:liu:diva-67516ISRN: LiTH-MAT-R–2011/08–SEOAI: diva2:410865
Available from: 2011-04-19 Created: 2011-04-15 Last updated: 2015-06-02Bibliographically approved

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