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Automated error control in finite element methods withapplications in fluid flow
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).
KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz). (Computational Technology Laboratory)ORCID iD: 0000-0003-4256-0463
2014 (English)Report (Other academic)
Abstract [en]

In this paper we present a new adaptive finite element method for thesolution of linear and non-linear partial differential equationsdirectly using the a posteriori error representation as a local errorindicator, with the primal and dual solutions approximated in the samefinite element space, here piecewise continuous linear functions onthe same mesh. Since this approach gives a global a posteriori errorrepresentation that is zero due to Galerkin orthogonality, the errorrepresentation has traditionally been thought to contain noinformation about the error. However, for elliptic andconvection-diffusion model problems we show the opposite, that locallythe orthogonal error representation behaves very similar to thenon-orthogonal error representation using a higher order approximationof the dual.  We have previously proved an a priori estimate of thelocal error indicator for elliptic problems, and in this paper weextend the proof to convection-reaction problems. We also present aversion of the method for non-elliptic and non-linear problems using astabilized finite element method where the a posteriori errorrepresentation is no longer orthogonal. We apply this method to thestationary incompressible Navier-Stokes equation and perform detailednumerical experiments which show that the a posteriori error estimateis within a factor 2 of the error based on a reference value on a finemesh, except in a few data points on very coarse meshes for anon-smooth test case where it is within a factor 3.

Place, publisher, year, edition, pages
2014.
Series
CTL Technical Report
Keyword [en]
FEM adaptivity a posteriori fluid mechanics
National Category
Computational Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-142410OAI: oai:DiVA.org:kth-142410DiVA: diva2:700166
Note

QC 20150422

Available from: 2014-03-03 Created: 2014-03-03 Last updated: 2015-04-22Bibliographically approved

Open Access in DiVA

No full text

Other links

http://www.csc.kth.se/~jjan/publications/sema-rep-adapt.pdf

Authority records BETA

Hoffman, Johan

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