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An adaptive finite element splitting method for the incompressible Navier–Stokes equations
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. (UMIT)
2012 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 209-212, 54-65 p.Article in journal (Refereed) Published
Abstract [en]

We present an adaptive finite element method for the incompressible Navier–Stokes equations based on a standard splitting scheme (the incremental pressure correction scheme). The presented method combines the efficiency and simplicity of a splitting method with the powerful framework offered by the finite element method for error analysis and adaptivity. An a posteriori error estimate is derived which expresses the error in a goal functional of interest as a sum of contributions from spatial discretization, time discretization and a term that measures the deviation of the splitting scheme from a pure Galerkin scheme (the computational error). Numerical examples are presented which demonstrate the performance of the adaptive algorithm and high quality efficiency indices. It is further demonstrated that the computational error of the Navier–Stokes momentum equation is linear in the size of the time step while the computational error of the continuity equation is quadratic in the size of the time step.

Place, publisher, year, edition, pages
2012. Vol. 209-212, 54-65 p.
Keyword [en]
Adaptive finite element method; A posteriori error estimate; Incompressible Navier–Stokes equations; Operator splitting method
National Category
Mathematics Engineering and Technology
Identifiers
URN: urn:nbn:se:umu:diva-51244DOI: 10.1016/j.cma.2011.10.002OAI: oai:DiVA.org:umu-51244DiVA: diva2:477888
Available from: 2012-01-14 Created: 2012-01-14 Last updated: 2017-12-08Bibliographically approved

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Larson, Mats G
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CiteExportLink to record
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  • apa
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  • de-DE
  • en-GB
  • en-US
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  • nn-NO
  • nn-NB
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  • Other locale
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Output format
  • html
  • text
  • asciidoc
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