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Adaptive mesh techniques based on a posteriori error estimates for an inverse Cauchy problem

Author

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  • Bergam, A.
  • Chakib, A.
  • Nachaoui, A.
  • Nachaoui, M.

Abstract

We are interested by an alternating method for an inverse Cauchy problem. Our main results of this paper consists in exhibiting local error indicators, based on a posteriori analysis, with respect to both space approximation and iterative algorithms. In contrast to existing results, the choice of adaptive finite element meshes will be considered after a comparison between the two kinds of indicators. This lead to an efficient method which have the ability to dramatically reduce the computational cost comparing with uniform grid refinement. Some numerical experiments support these results.

Suggested Citation

  • Bergam, A. & Chakib, A. & Nachaoui, A. & Nachaoui, M., 2019. "Adaptive mesh techniques based on a posteriori error estimates for an inverse Cauchy problem," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 865-878.
    • Handle: RePEc:eee:apmaco:v:346:y:2019:i:c:p:865-878
    DOI: 10.1016/j.amc.2018.09.069
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    References listed on IDEAS

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    1. Ellabib, A. & Nachaoui, A., 2008. "An iterative approach to the solution of an inverse problem in linear elasticity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(2), pages 189-201.
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    Cited by:

    1. Syrym E. Kasenov & Aigerim M. Tleulesova & Ainur E. Sarsenbayeva & Almas N. Temirbekov, 2024. "Numerical Solution of the Cauchy Problem for the Helmholtz Equation Using Nesterov’s Accelerated Method," Mathematics, MDPI, vol. 12(17), pages 1-20, August.
    2. Xi, Qiang & Fu, Zhuojia & Wu, Wenjie & Wang, Hui & Wang, Yong, 2021. "A novel localized collocation solver based on Trefftz basis for potential-based inverse electromyography," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    3. Ellabib, Abdellatif & Nachaoui, Abdeljalil & Ousaadane, Abdessamad, 2021. "Mathematical analysis and simulation of fixed point formulation of Cauchy problem in linear elasticity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 231-247.

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    1. Ellabib, Abdellatif & Nachaoui, Abdeljalil & Ousaadane, Abdessamad, 2021. "Mathematical analysis and simulation of fixed point formulation of Cauchy problem in linear elasticity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 231-247.

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