First-order system least squares on curved boundaries: Lowest-order Raviart-Thomas elements

Fleurianne Bertrand, Steffen Münzenmaier, Gerhard Starke

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Abstract

The effect of interpolated edges of curved boundaries on Raviart--Thomas finite element approximations is studied in this paper in the context of first-order system least squares methods. In particular, it is shown that an optimal order of convergence is achieved for lowest-order elements on a polygonal domain. This is illustrated numerically for an elliptic boundary value problem involving circular curves. The computational results also show that a polygonal approximation is not sufficient to achieve convergence of optimal order in the higher-order case.
Original languageEnglish
Pages (from-to)880-894
JournalSIAM Journal on Numerical Analysis
Volume52
Issue number2
DOIs
Publication statusPublished - 2014
Externally publishedYes

Keywords

  • Interpolated boundaries
  • Raviart-Thomas spaces
  • First-order system least-squares

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