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Adaptive error control in finite element methods using the error representation as error indicator
KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz). (Computational Technology Laboratory)ORCID iD: 0000-0002-1695-8809
KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz). (Computational Technology Laboratory)ORCID iD: 0000-0003-4256-0463
KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz). (Computational Technology Laboratory)
2013 (English)Report (Other academic)
Abstract [en]

In this paper we present a new a posteriori adaptive finite elementmethod (FEM) directly using the error representation as a local errorindicator, and representing the primal and dual solutions in the samefinite element space (here piecewise continuous linear functions onthe same mesh). Since this approach gives a global a posteriori errorestimate that is zero (due to the Galerkin orthogonality), the errorrepresentation has historically been thought to contain no informationabout the error. However, we show the opposite, that locally, theorthogonal error representation behaves very similar to thenon-orthogonal error representation using a quadratic approximation ofthe dual. We present evidence of this both in the form of an a prioriestimate for the local error indicator and a detailed computationalinvestigation showing that the two methods exhibit very similarbehavior and performance, and thus confirming the theoreticalprediction. We also present a stabilized version of the method fornon-elliptic partial differential equations (PDE) where the errorrepresentation is no longer orthogonal, and where both the local errorindicator and global error estimate behave similar to the errorrepresentation using a quadratic approximation of the dual.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2013. , 21 p.
Series
CTL Technical Report
Keyword [en]
FEM adaptivity stabilized
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-134038OAI: oai:DiVA.org:kth-134038DiVA: diva2:664443
Note

QC 20131118

Available from: 2013-11-15 Created: 2013-11-15 Last updated: 2013-11-18Bibliographically approved

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