Solution of the inverse elastography problem for parametric classes of inclusions with a posteriori error estimate

DOI10.1515/JIIP-2017-0043zbMath1397.65237OpenAlexW2757019705MaRDI QIDQ1654219

Alexander S. Leonov, Anatoly G. Yagola, Alexander N. Sharov

Publication date: 7 August 2018

Published in: Journal of Inverse and Ill-Posed Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/jiip-2017-0043

zbMATH Keywords

inverse problemYoung's modulusa posteriori error estimateelastographyquasisolution

Mathematics Subject Classification ID

Linear elasticity with initial stresses (74B10) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) 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 methods for ill-posed problems for boundary value problems involving PDEs (65N20)

Related Items (3)

Solution of the two-dimensional inverse problem of quasistatic elastography with the help of the small parameter method ⋮ Extra-optimal methods for solving ill-posed problems: survey of theory and examples ⋮ Calculation of the gradient of Tikhonov's functional in solving coefficient inverse problems for linear partial differential equations

Cites Work

• A posteriori error estimates for approximate solutions of irregular operator equations
• Locally extra-optimal regularizing algorithms and a posteriori estimates of the accuracy for ill-posed problems with discontinuous solutions
• A posteriori error estimates for numerical solutions to inverse problems of elastography
• Error estimation for ill-posed problems on piecewise convex functions and sourcewise represented sets
• Solution of inverse problems in elasticity imaging using the adjoint method
• Elastic modulus imaging: on the uniqueness and nonuniqueness of the elastography inverse problem in two dimensions
• Extra-optimal methods for solving ill-posed problems
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