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Computable Error Indicators for Approximate Solutions of Elliptic Problems

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ECCOMAS Multidisciplinary Jubilee Symposium

Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 14))

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The paper is concerned with computable indicators of approximation errors. With the paradigm of a linear elliptic problem we discuss new error indicators that can be used in mesh-adaptive numerical methods. Indicators of the first type follow from functional a posteriori estimates. They indicate the distribution of errors in the whole computational domain. Another group of indicators is focused on the so-called goal-oriented error functionals typically associated with some sub-domains where the accuracy of an approximate solution is especially important. Usually, indicators of this type use solutions of adjoint boundary value problems. We obtain a new exact form of the goal-oriented linear functional with the help of which derive two new error indicators. They do not exploit extra regularity of adjoint solutions and special properties of the respective approximations (as, e.g., superconvergence). Finally, the paper suggests an error indicator, which is based not on finite element approximations of adjoint problems but on modifications of solutions known for some “etalon” domains.

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Authors and Affiliations

  1. Department of Mathematical Information Technology, University of Jyväskylä, P.O. Box 35, FIN-40014;, (Agora)

    P. Neittaanmäki

  2. St. Petersburg Department of V. A. Steklov Institute of Mathematics, St. Petersburg, Fontanka, 27, 191023, Russian Federation

    S. Repin

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  1. P. Neittaanmäki
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  2. S. Repin
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Editors and Affiliations

  1. Institute for Mechanics of Materials and Structures, Vienna University of Technology, Vienna, Austria

    Josef Eberhardsteiner , Christian Hellmich  & Herbert A. Mang ,  & 

  2. CIMNE, Barcelona, Spain

    Jacques Périaux

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Neittaanmäki, P., Repin, S. (2009). Computable Error Indicators for Approximate Solutions of Elliptic Problems. In: Eberhardsteiner, J., Hellmich, C., Mang, H.A., Périaux, J. (eds) ECCOMAS Multidisciplinary Jubilee Symposium. Computational Methods in Applied Sciences, vol 14. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9231-2_14

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  • DOI: https://doi.org/10.1007/978-1-4020-9231-2_14

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