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A posteriori-driven adaptive strategy for solving inverse Cauchy problems in diffusion-reaction models

Author

Listed:
  • Hamdi, Hafida
  • Nachaoui, Mourad
  • Bergam, Amal
  • Nachaoui, Abdeljalil

Abstract

This work addresses the inverse Cauchy problem for the modified Helmholtz equation using an alternating iterative approach. The central contribution lies in the design of novel local error indicators based on a posteriori analysis, which simultaneously assess the accuracy of the spatial discretization and the convergence behavior of the iterative algorithm. Unlike standard methods, our strategy leverages a comparative assessment of these indicators to drive an adaptive mesh refinement process. This adaptive framework ensures a more balanced distribution of computational resources, significantly reducing the numerical cost while maintaining high solution accuracy. The proposed methodology is validated through a series of synthetic and application-driven numerical experiments, demonstrating both its effectiveness and robustness in reconstructing inaccessible boundary data.

Suggested Citation

  • Hamdi, Hafida & Nachaoui, Mourad & Bergam, Amal & Nachaoui, Abdeljalil, 2026. "A posteriori-driven adaptive strategy for solving inverse Cauchy problems in diffusion-reaction models," Applied Mathematics and Computation, Elsevier, vol. 518(C).
    • Handle: RePEc:eee:apmaco:v:518:y:2026:i:c:s0096300325006277
    DOI: 10.1016/j.amc.2025.129902
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