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Journal of Scientific Computing

, Volume 71, Issue 1, pp 329–347 | Cite as

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

  • Christine Bernardi
  • Jad Dakroub
  • Gihane Mansour
  • Farah Rafei
  • Toni Sayah
Article

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.

Keywords

Posteriori error estimation Nonlinear problems Iterative methods Finite elements method 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Christine Bernardi
    • 1
  • Jad Dakroub
    • 1
    • 2
  • Gihane Mansour
    • 2
  • Farah Rafei
    • 2
  • Toni Sayah
    • 2
  1. 1.Laboratoire Jacques-Louis Lions - C.N.R.S.Université Pierre et Marie CurieParis Cedex 05France
  2. 2.Unité de recherche EGFEM, Faculté des sciencesUniversité Saint-JosephBeirutLebanon

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