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A posteriori analysis of iterative algorithms for a nonlinear problem

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Abstract

A posteriori error indicators have been studied in recent years owing to their remarkable capacity to enhance both speed and accuracy in computing. This work deals with a posteriori error estimation for the finite element discretization of a nonlinear problem. For a given nonlinear equation considering finite elements we solve the discrete problem using iterative methods involving some kind of linearization. For each of them, there are actually two sources of error, namely discretization and linearization. Balancing these two errors can be very important, since it avoids performing an excessive number of iterations. Our results lead to the construction of computable upper indicators for the full error. Several numerical tests are provided to evaluate the efficiency of our indicators.

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Authors and Affiliations

  1. Laboratoire Jacques-Louis Lions, C. N. R. S., Université Pierre et Marie Curie, B.C. 187, 4 place Jussieu, 75252, Paris Cedex 05, France

    Christine Bernardi

  2. Faculté des Sciences, Université Saint-Joseph, B.P 11-514, Riad El Solh, Beirut, 1107 2050, Lebanon

    Jad Dakroub, Gihane Mansour & Toni Sayah

Authors
  1. Christine Bernardi
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  2. Jad Dakroub
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  3. Gihane Mansour
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  4. Toni Sayah
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Correspondence to Christine Bernardi.

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Bernardi, C., Dakroub, J., Mansour, G. et al. A posteriori analysis of iterative algorithms for a nonlinear problem. J Sci Comput 65, 672–697 (2015). https://doi.org/10.1007/s10915-014-9980-4

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  • DOI: https://doi.org/10.1007/s10915-014-9980-4

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