Convergence rates for Tikhonov regularization of a two-coefficient identification problem in an elliptic boundary value problem

DOI10.1007/s00211-011-0406-zzbMath1241.65093OpenAlexW2008377696MaRDI QIDQ663263

Tran Nhan Tam Quyen, Dinh Nho Hào

Publication date: 14 February 2012

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-011-0406-z

zbMATH Keywords

convergenceTikhonov regularizationnonlinear ill-posed problemsspatially varying coefficientsinverse elliptic problemconvex energy functionalsweak source condition

Mathematics Subject Classification ID

Ill-posed problems for PDEs (35R25) Inverse problems for PDEs (35R30) Nonlinear elliptic equations (35J60) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20)

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Direct method for solving the inverse coefficient problem ⋮ Sparsity regularization of the diffusion coefficient identification problem: well-posedness and convergence rates ⋮ On two-coefficient identification in elliptic variational inequalities ⋮ Reconstructing conductivity coefficients based on sparsity regularization and measured data in electrical impedance tomography ⋮ Inverse problems with nonnegative and sparse solutions: algorithms and application to the phase retrieval problem ⋮ Descent gradient methods for nonsmooth minimization problems in ill-posed problems ⋮ Variational method for multiple parameter identification in elliptic PDEs ⋮ Determining two coefficients in diffuse optical tomography with incomplete and noisy Cauchy data ⋮ A reaction coefficient identification problem for fractional diffusion ⋮ Convergence rates for total variation regularization of coefficient identification problems in elliptic equations. II ⋮ Heuristic discrepancy principle for variational regularization of inverse problems ⋮ Finite element analysis for identifying the reaction coefficient in PDE from boundary observations ⋮ Inverse problems for nonlinear quasi-variational hemivariational inequalities with application to obstacle problems of elliptic type ⋮ Dynamic force identification problem based on a novel improved Tikhonov regularization method ⋮ Finite element methods for coefficient identification in an elliptic equation

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