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Goal Oriented, Anisotropic, A Posteriori Error Estimates for the Laplace Equation

In: Numerical Mathematics and Advanced Applications 2009

Author

Listed:
  • Frederic Alauzet

    (INRIA Rocquencourt, Projet Gamma)

  • Wissam Hassan

    (IACS, Station 8, Ecole Polytechnique Fédérale de Lausanne)

  • Marco Picasso

    (INRIA Rocquencourt, Projet Gamma
    IACS, Station 8, Ecole Polytechnique Fédérale de Lausanne)

Abstract

A posteriori error estimates are presented for the Laplace equation and meshes with large aspect ratio. Error estimates are presented in the natural H 1 seminorm or in the framework of goal oriented error control. The proposed estimator relies on anisotropic interpolation estimates derived by Formaggia and Perotto [Numer. Math. 89(4), 641–667 (2001), Numer. Math. 94(1), 67–92 (2003)] and on Zienckiewicz–Zhu [Int. J. Numer. Meth. Eng. 33(7), 1331–1364 (1992), Int. J. Numer. Meth. Eng. 24(2), 337–357 (1987)] post-processing techniques, thus avoids approximations of the Hessian of the solution. All the constant involved in the error estimates are independent of the mesh size and aspect ratio, which should enable the use of anisotropic, adaptive finite elements.

Suggested Citation

  • Frederic Alauzet & Wissam Hassan & Marco Picasso, 2010. "Goal Oriented, Anisotropic, A Posteriori Error Estimates for the Laplace Equation," Springer Books, in: Gunilla Kreiss & Per Lötstedt & Axel Målqvist & Maya Neytcheva (ed.), Numerical Mathematics and Advanced Applications 2009, pages 47-58, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-11795-4_4
    DOI: 10.1007/978-3-642-11795-4_4
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