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

Frederic Alauzet (), Wissam Hassan () and Marco Picasso ()
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Frederic Alauzet: INRIA Rocquencourt, Projet Gamma
Wissam Hassan: IACS, Station 8, Ecole Polytechnique Fédérale de Lausanne
Marco Picasso: INRIA Rocquencourt, Projet Gamma

A chapter in Numerical Mathematics and Advanced Applications 2009, 2010, pp 47-58 from Springer

Abstract: 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.

Keywords: Error Estimator; Laplace Equation; Posteriori Error; Isotropic Setting; Large Aspect Ratio (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/978-3-642-11795-4_4

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