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Automated error con...
Automated error control in finite element methods withapplications in fluid flow
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- Jansson, Johan, 1978- (författare)
- KTH,High Performance Computing and Visualization (HPCViz),Computational Technology Laboratory
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- Spühler, Jeannette (författare)
- KTH,High Performance Computing and Visualization (HPCViz)
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- Degirmenci, Cem (författare)
- KTH,High Performance Computing and Visualization (HPCViz)
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- Hoffman, Johan (författare)
- KTH,High Performance Computing and Visualization (HPCViz),Computational Technology Laboratory
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(creator_code:org_t)
- 2014
- Engelska.
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Serie: CTL Technical Report
- Relaterad länk:
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http://www.csc.kth.s...
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https://urn.kb.se/re...
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Abstract
Ämnesord
Stäng
- 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.
Ämnesord
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Nyckelord
- FEM adaptivity a posteriori fluid mechanics
- Mathematics
- Matematik
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