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Adaptive error control in finite element methods using the error representation as error indicator
KTH, Skolan för datavetenskap och kommunikation (CSC), High Performance Computing and Visualization (HPCViz). (Computational Technology Laboratory)ORCID-id: 0000-0002-1695-8809
KTH, Skolan för datavetenskap och kommunikation (CSC), High Performance Computing and Visualization (HPCViz). (Computational Technology Laboratory)ORCID-id: 0000-0003-4256-0463
KTH, Skolan för datavetenskap och kommunikation (CSC), High Performance Computing and Visualization (HPCViz). (Computational Technology Laboratory)
2013 (engelsk)Rapport (Annet vitenskapelig)
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.

sted, utgiver, år, opplag, sider
KTH Royal Institute of Technology, 2013. , s. 21
Serie
CTL Technical Report
Emneord [en]
FEM adaptivity stabilized
HSV kategori
Identifikatorer
URN: urn:nbn:se:kth:diva-134038OAI: oai:DiVA.org:kth-134038DiVA, id: diva2:664443
Merknad

QC 20131118

Tilgjengelig fra: 2013-11-15 Laget: 2013-11-15 Sist oppdatert: 2013-11-18bibliografisk kontrollert

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representation-adaptivity.pdf(5860 kB)327 nedlastinger
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Hoffman, Johan

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