A posteriori error estimates for numerical solutions to inverse problems of elastography

DOI10.1080/17415977.2016.1138949zbMath1359.74421OpenAlexW2291413871MaRDI QIDQ2971538

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

Publication date: 5 April 2017

Published in: Inverse Problems in Science and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17415977.2016.1138949

zbMATH Keywords

regularizationa posteriori error estimateselastographyYoung's modulus reconstruction

Mathematics Subject Classification ID

Finite element methods applied to problems in solid mechanics (74S05) Inverse problems for waves in solid mechanics (74J25)

Related Items (6)

Solution of the two-dimensional inverse problem of quasistatic elastography with the help of the small parameter method ⋮ Solution of the inverse elastography problem for parametric classes of inclusions with a posteriori error estimate ⋮ ``Fast solution of the three-dimensional inverse problem of quasi-static elastography with the help of the small parameter method ⋮ Extra-optimal methods for solving ill-posed problems: survey of theory and examples ⋮ Solution of the three-dimensional inverse elastography problem for parametric classes of inclusions ⋮ 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
• Scatter Search and Local NLP Solvers: A Multistart Framework for Global Optimization
• Encyclopedia of Optimization
• Analysis of bounded variation penalty methods for ill-posed problems
• Solution of inverse problems in elasticity imaging using the adjoint method
• The problems of linear and quadratic programming for ill-posed problems on some compact sets
• Numerical piecewise-uniform regularization for two-dimensional ill-posed problems
• A posteriori accuracy estimations of solutions to ill-posed inverse problems and extra-optimal regularizing algorithms for their solution

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