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Convergence Analysis of Two Numerical Schemes Applied to a Nonlinear Elliptic Problem

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Abstract

For a given nonlinear problem discretized by standard finite elements, we propose two iterative schemes to solve the discrete problem. We prove the well-posedness of the corresponding problems and their convergence. Next, we construct error indicators and prove optimal a posteriori estimates where we treat separately the discretization and linearization errors. Some numerical experiments confirm the validity of the schemes and allow us to compare them.

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Authors and Affiliations

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

    Christine Bernardi & Jad Dakroub

  2. Unité de recherche EGFEM, Faculté des sciences, Université Saint-Joseph, Beirut, Lebanon

    Jad Dakroub, Gihane Mansour, Farah Rafei & 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. Farah Rafei
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  5. Toni Sayah
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Corresponding author

Correspondence to Toni Sayah.

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Bernardi, C., Dakroub, J., Mansour, G. et al. Convergence Analysis of Two Numerical Schemes Applied to a Nonlinear Elliptic Problem. J Sci Comput 71, 329–347 (2017). https://doi.org/10.1007/s10915-016-0301-y

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  • DOI: https://doi.org/10.1007/s10915-016-0301-y

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