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May 24, 2026Knowledge Engineering and Data ScienceOpen Access

Stable Numerical Solution of an Elliptic PDE Inverse Problem Subject to Incomplete Boundary Conditions

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Authors

QTQasim Abd Ali TayyehSouthern Technical University

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Implication

Randomized trial shows effective reconstruction of model parameters in complex geometries, suggesting practical applications in medical imaging and engineering.

Key Points

  • This research aims to develop a numerical framework for solving inverse elliptic PDEs with incomplete boundary data.
  • Utilized a finite element method to discretize the variational problem.
  • Employed Tikhonov regularization and adjoint-based optimization to solve the problem.
  • Applied Morozov's Discrepancy Principle to determine optimal regularization parameters.
  • Successfully reconstructed unknown model parameters with less than 5% L2 error even with 5% noise in measurements.
  • The method demonstrates robustness across various domain geometries, including complex shapes.
  • Framework is applicable in fields such as medical imaging, geophysics, and engineering diagnostics.

Cite This Study

Qasim Abd Ali Tayyeh (2025) studied this question.

synapsesocial.com/papers/6a12968148a0ea16656735a8https://doi.org/10.17977/um018v8i22025p215-230
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Stable Numerical Solution of an Elliptic PDE Inverse Problem Subject to Incomplete Boundary Conditions2025
  2. 2Approximating partial differential equations without boundary conditions2024
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  4. 4Generalized Tikhonov regularization method for an inverse boundary value problem of the fractional elliptic equation2024 · 2 citations
  5. 5A unified variational framework for elliptic PDEs with mixed Dirichlet–Neumann boundary conditions2026