Adaptivity with relaxation for ill-posed problems and global convergence for a coefficient inverse problem

DOI10.1007/s10958-010-9921-1zbMath1286.65147OpenAlexW2091826848MaRDI QIDQ2448925

Larisa Beilina, Michael V. Klibanov, Mikhail Yu. Kokurin

Publication date: 5 May 2014

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-010-9921-1

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Numerical solution to inverse problems in abstract spaces (65J22)

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Uses Software

• TIGRA

Cites Work

• The boundary value problems of mathematical physics. Transl. from the Russian by Jack Lohwater
• Carleman estimates for coefficient inverse problems and numerical applications.
• Synthesis of global convergence and adaptivity for a hyperbolic coefficient inverse problem in 3D
• A gradient descent method for solving an inverse coefficient heat conduction problem
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• A posteriori error estimates for the adaptivity technique for the Tikhonov functional and global convergence for a coefficient inverse problem
• Simultaneous determination of the source terms in a linear hyperbolic problem from the final overdetermination: weak solution approach
• Inverse problems and Carleman estimates
• Absorbing Boundary Conditions for the Numerical Simulation of Waves
• TIGRA an iterative algorithm for regularizing nonlinear ill-posed problems
• Hybrid FEM/FDM method for an inverse scattering problem
• A steepest descent algorithm for the global minimization of the Tikhonov functional
• Inverse problems for a perturbed dissipative half-space
• A Globally Convergent Numerical Method for a Coefficient Inverse Problem
• MUSIC‐Type Electromagnetic Imaging of a Collection of Small Three‐Dimensional Inclusions
• Efficient computation of the Tikhonov regularization parameter by goal-oriented adaptive discretization
• An Adaptive Hybrid FEM/FDM Method for an Inverse Scattering Problem in Scanning Acoustic Microscopy
• Lipschitz stability of an inverse problem for an acoustic equation
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