A variational method for parameter identification
ESAIM: M2AN, 22 1 (1988) 119-158
Published online: 2017-01-31
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
NN‐mCRE: A modified constitutive relation error framework for unsupervised learning of nonlinear state laws with physics‐augmented neural networks
Antoine Benady, Emmanuel Baranger and Ludovic ChamoinInternational Journal for Numerical Methods in Engineering 125 (8) (2024)
https://doi.org/10.1002/nme.7439
Conductivity Imaging from Internal Measurements with Mixed Least-Squares Deep Neural Networks
Bangti Jin, Xiyao Li, Qimeng Quan and Zhi ZhouSIAM Journal on Imaging Sciences 17 (1) 147 (2024)
https://doi.org/10.1137/23M1562536
Convergence rate analysis of Galerkin approximation of inverse potential problem
Bangti Jin, Xiliang Lu, Qimeng Quan and Zhi ZhouInverse Problems 39 (1) 015008 (2023)
https://doi.org/10.1088/1361-6420/aca70e
Identification of the heterogeneous conductivity in an inverse heat conduction problem
Angel A. Ciarbonetti, Sergio Idelsohn and Ruben D. SpiesInternational Journal for Numerical Methods in Engineering 124 (5) 1128 (2023)
https://doi.org/10.1002/nme.7156
On uniqueness and stable estimation of multiple parameters in the Cahn–Hilliard equation
Aaron Brunk, Herbert Egger and Oliver HabrichInverse Problems 39 (6) 065002 (2023)
https://doi.org/10.1088/1361-6420/acca44
The diffusion identification in a SIS reaction-diffusion system
Aníbal Coronel, Fernando Huancas, Ian Hess and Alex TelloMathematical Biosciences and Engineering 21 (1) 562 (2023)
https://doi.org/10.3934/mbe.2024024
mCRE-based parameter identification from full-field measurements: Consistent framework, integrated version, and extension to nonlinear material behaviors
Hai Nam Nguyen, Ludovic Chamoin and Cuong Ha MinhComputer Methods in Applied Mechanics and Engineering 400 115461 (2022)
https://doi.org/10.1016/j.cma.2022.115461
Imaging Anisotropic Conductivities from Current Densities
Huan Liu, Bangti Jin and Xiliang LuSIAM Journal on Imaging Sciences 15 (2) 860 (2022)
https://doi.org/10.1137/21M1437810
Error Analysis of Finite Element Approximations of Diffusion Coefficient Identification for Elliptic and Parabolic Problems
Bangti Jin and Zhi ZhouSIAM Journal on Numerical Analysis 59 (1) 119 (2021)
https://doi.org/10.1137/20M134383X
An ADMM-Newton-CNN numerical approach to a TV model for identifying discontinuous diffusion coefficients in elliptic equations: convex case with gradient observations
Wenyi Tian, Xiaoming Yuan and Hangrui YueInverse Problems 37 (8) 085004 (2021)
https://doi.org/10.1088/1361-6420/ac0e80
Neural networks as smooth priors for inverse problems for PDEs
Jens Berg and Kaj NyströmJournal of Computational Mathematics and Data Science 1 100008 (2021)
https://doi.org/10.1016/j.jcmds.2021.100008
Consistency of Bayesian inference with Gaussian process priors in an elliptic inverse problem
Matteo Giordano and Richard NicklInverse Problems 36 (8) 085001 (2020)
https://doi.org/10.1088/1361-6420/ab7d2a
Determining two coefficients in diffuse optical tomography with incomplete and noisy Cauchy data
Tran Nhan Tam QuyenInverse Problems 36 (9) 095011 (2020)
https://doi.org/10.1088/1361-6420/aba5f0
Finite element analysis for identifying the reaction coefficient in PDE from boundary observations
Tran Nhan Tam QuyenApplied Numerical Mathematics 145 297 (2019)
https://doi.org/10.1016/j.apnum.2019.06.015
Analysis of the Error in Constitutive Equation Approach for Time-Harmonic Elasticity Imaging
Wilkins Aquino and Marc BonnetSIAM Journal on Applied Mathematics 79 (3) 822 (2019)
https://doi.org/10.1137/18M1231237
Static damage identification in beams by minimum constitutive relation error
Jia Guo, Li Wang and Izuru TakewakiInverse Problems in Science and Engineering 27 (10) 1347 (2019)
https://doi.org/10.1080/17415977.2018.1553965
Variational method for multiple parameter identification in elliptic PDEs
Tran Nhan Tam QuyenJournal of Mathematical Analysis and Applications 461 (1) 676 (2018)
https://doi.org/10.1016/j.jmaa.2018.01.030
Diffusion Coefficients Estimation for Elliptic Partial Differential Equations
Andrea Bonito, Albert Cohen, Ronald DeVore, Guergana Petrova and Gerrit WelperSIAM Journal on Mathematical Analysis 49 (2) 1570 (2017)
https://doi.org/10.1137/16M1094476
Sparsity Regularization of the Diffusion Coefficient Identification Problem: Well-Posedness and Convergence Rates
Pham Quy MuoiBulletin of the Malaysian Mathematical Sciences Society 39 (3) 1145 (2016)
https://doi.org/10.1007/s40840-015-0226-x
Descent gradient methods for nonsmooth minimization problems in ill-posed problems
Pham Quy Muoi, Dinh Nho Hào, Peter Maass and Michael PidcockJournal of Computational and Applied Mathematics 298 105 (2016)
https://doi.org/10.1016/j.cam.2015.11.039
Matrix coefficient identification in an elliptic equation with the convex energy functional method
Michael Hinze and Tran Nhan Tam QuyenInverse Problems 32 (8) 085007 (2016)
https://doi.org/10.1088/0266-5611/32/8/085007
Three-dimensional transient elastodynamic inversion using the modified error in constitutive relation
Marc Bonnet and Wilkins AquinoJournal of Physics: Conference Series 542 012003 (2014)
https://doi.org/10.1088/1742-6596/542/1/012003
Finite element methods for coefficient identification in an elliptic equation
Dinh Nho Hào and Tran Nhan Tam QuyenApplicable Analysis 93 (7) 1533 (2014)
https://doi.org/10.1080/00036811.2013.840365
Reconstruction of constitutive parameters in isotropic linear elasticity from noisy full-field measurements
Guillaume Bal, Cédric Bellis, Sébastien Imperiale and François MonardInverse Problems 30 (12) 125004 (2014)
https://doi.org/10.1088/0266-5611/30/12/125004
275 (2013)
https://doi.org/10.1002/9781118578469.ch10
Convergence rates for total variation regularization of coefficient identification problems in elliptic equations II
Dinh Nho Hào and Tran Nhan Tam QuyenJournal of Mathematical Analysis and Applications 388 (1) 593 (2012)
https://doi.org/10.1016/j.jmaa.2011.11.008
Convergence and error analysis of a numerical method for the identification of matrix parameters in elliptic PDEs
Klaus Deckelnick and Michael HinzeInverse Problems 28 (11) 115015 (2012)
https://doi.org/10.1088/0266-5611/28/11/115015
Convergence rates for Tikhonov regularization of a two-coefficient identification problem in an elliptic boundary value problem
Dinh Nho Hào and Tran Nhan Tam QuyenNumerische Mathematik 120 (1) 45 (2012)
https://doi.org/10.1007/s00211-011-0406-z
Stability and error estimates for an equation error method for elliptic equations
Mohammad F Al-Jamal and Mark S GockenbachInverse Problems 28 (9) 095006 (2012)
https://doi.org/10.1088/0266-5611/28/9/095006
Convergence rates for total variation regularization of coefficient identification problems in elliptic equations I
Dinh Nho Hào and Tran Nhan Tam QuyenInverse Problems 27 (7) 075008 (2011)
https://doi.org/10.1088/0266-5611/27/7/075008
Convergence rates for Tikhonov regularization of coefficient identification problems in Laplace-type equations
Dinh Nho Hào and Tran Nhan Tam QuyenInverse Problems 26 (12) 125014 (2010)
https://doi.org/10.1088/0266-5611/26/12/125014
Enriched kinematic fields of cracked structures
Carole Henninger, Stéphane Roux and François HildInternational Journal of Solids and Structures 47 (24) 3305 (2010)
https://doi.org/10.1016/j.ijsolstr.2010.08.012
Topological sensitivity of energy cost functional for wave-based defect identification
Marc BonnetComptes Rendus Mécanique 338 (7-8) 377 (2010)
https://doi.org/10.1016/j.crme.2010.07.016
On the inverse problem of identifying Lamé coefficients in linear elasticity
B. Jadamba, A.A. Khan and F. RacitiComputers & Mathematics with Applications 56 (2) 431 (2008)
https://doi.org/10.1016/j.camwa.2007.12.016
Equation error approach for elliptic inverse problems with an application to the identification of Lamé parameters
M. S. Gockenbach, B. Jadamba and A. A. KhanInverse Problems in Science and Engineering 16 (3) 349 (2008)
https://doi.org/10.1080/17415970701602580
Mechanical Properties of Crimped Mineral Wools: Identification From Digital Image Correlation
Jean-François Witz, Stéphane Roux, François Hild and Jean-Baptiste RieunierJournal of Engineering Materials and Technology 130 (2) (2008)
https://doi.org/10.1115/1.2884575
Numerical analysis of elliptic inverse problems with interior data
M S GockenbachJournal of Physics: Conference Series 124 012026 (2008)
https://doi.org/10.1088/1742-6596/124/1/012026
Identification of elastic property and loading fields from full-field displacement measurements
F. Amiot, F. Hild and J.P. RogerInternational Journal of Solids and Structures 44 (9) 2863 (2007)
https://doi.org/10.1016/j.ijsolstr.2006.08.031
Identification of the electroelastic coupling from full multi-physical fields measured at the micrometre scale
F Amiot, F Hild, F Kanoufi and J P RogerJournal of Physics D: Applied Physics 40 (11) 3314 (2007)
https://doi.org/10.1088/0022-3727/40/11/009
Identification of a Damage Law by Using Full-field Displacement Measurements
Damien Claire, François Hild and Stéphane RouxInternational Journal of Damage Mechanics 16 (2) 179 (2007)
https://doi.org/10.1177/1056789506064940
The output least-squares approach to estimating Lamé moduli
Mark S GockenbachInverse Problems 23 (6) 2437 (2007)
https://doi.org/10.1088/0266-5611/23/6/010
Estimating thermal conductivities from temperature maps using wavelets
Stéphane Roux and dos Santos Liacir LucenaInverse Problems in Science and Engineering 14 (8) 785 (2006)
https://doi.org/10.1080/17415970600731035
Solving Cauchy problems by minimizing an energy-like functional
S Andrieux, T N Baranger and A Ben AbdaInverse Problems 22 (1) 115 (2006)
https://doi.org/10.1088/0266-5611/22/1/007
A stress scale in full-field identification procedures: a diffuse stress gauge
Stéphane Roux, François Hild and Stéphane PaganoEuropean Journal of Mechanics - A/Solids 24 (3) 442 (2005)
https://doi.org/10.1016/j.euromechsol.2005.02.002
Inverse problems in elasticity
Marc Bonnet and Andrei ConstantinescuInverse Problems 21 (2) R1 (2005)
https://doi.org/10.1088/0266-5611/21/2/R01
Transmissivity estimation for a two-dimensional aquifer by regularizing potential and stream functions
Jun Liu and G Q ZhangInverse Problems 20 (2) 331 (2004)
https://doi.org/10.1088/0266-5611/20/2/002
A finite element formulation to identify damage fields: the equilibrium gap method
D. Claire, F. Hild and S. RouxInternational Journal for Numerical Methods in Engineering 61 (2) 189 (2004)
https://doi.org/10.1002/nme.1057
Identification of damage fields using kinematic measurements
Damien Claire, François Hild and Stéphane RouxComptes Rendus. Mécanique 330 (11) 729 (2002)
https://doi.org/10.1016/S1631-0721(02)01524-3
A Variational Method for Recovering Planar Lamé Moduli
Jun Chen and Mark S. GockenbachMathematics and Mechanics of Solids 7 (2) 191 (2002)
https://doi.org/10.1177/1081286502007002221
Identification of elastic parameters by displacement field measurement
Giuseppe Geymonat, François Hild and Stéphane PaganoComptes Rendus. Mécanique 330 (6) 403 (2002)
https://doi.org/10.1016/S1631-0721(02)01476-6
Parameter identification for elliptic problems
Ian KnowlesJournal of Computational and Applied Mathematics 131 (1-2) 175 (2001)
https://doi.org/10.1016/S0377-0427(00)00275-2
Robust reconstruction of a physical parameter distribution using fewer field measurements of another physical variable: resolution of the problem of determination of conductivity
C Sumi and H KoMeasurement Science and Technology 12 (5) 589 (2001)
https://doi.org/10.1088/0957-0233/12/5/306
A mixed least-squares method for an inverse problem of a nonlinear beam equation
Richard E Ewing, Tao Lin and Yanping LinInverse Problems 15 (1) 19 (1999)
https://doi.org/10.1088/0266-5611/15/1/006
Identification of the Friction Coefficient in Shallow-Water Flows Using Optimal Control Theory
A. SOULAIMANI and M. IDRISSIInternational Journal of Computational Fluid Dynamics 12 (1) 29 (1999)
https://doi.org/10.1080/10618569908940814
A numerical method for parameter identification of a boundary value problem
Tao Lin and Edgardo RamirezApplicable Analysis 69 (3-4) 349 (1998)
https://doi.org/10.1080/00036819808840667
A C0 finite element method for an inverse problem
Tao LinApplied Mathematics and Computation 90 (2-3) 253 (1998)
https://doi.org/10.1016/S0096-3003(97)00401-3
An inverse problem from 2D ground-water modelling
G Bruckner, S Handrock-Meyer and H LangmachInverse Problems 14 (4) 835 (1998)
https://doi.org/10.1088/0266-5611/14/4/005
Denoising with higher order derivatives of bounded variation and an application to parameter estimation
O. ScherzerComputing 60 (1) 1 (1998)
https://doi.org/10.1007/BF02684327
Un problème d'identification de paramètre associé aux équations de Saint-Venant
Mekki Idrissi and Azzeddine SoulaimaniRevue Européenne des Éléments Finis 6 (4) 399 (1997)
https://doi.org/10.1080/12506559.1997.10511283
An equation error method to recover diffusion from the distributed observation
Tommi KärkkäinenInverse Problems 13 (4) 1033 (1997)
https://doi.org/10.1088/0266-5611/13/4/009
Recovering Planar Lame Moduli from a Single-Traction Experiment
Steven J. Cox and Mark GockenbachMathematics and Mechanics of Solids 2 (3) 297 (1997)
https://doi.org/10.1177/108128659700200304
Numerical methods for nonlinear inverse problems
T. Kärkkäinen, P. Neittaanmäki and A. NiemistöJournal of Computational and Applied Mathematics 74 (1-2) 231 (1996)
https://doi.org/10.1016/0377-0427(96)00026-X
A variational solution for the aquifer transmissivity problem
Ian Knowles and Robert WallaceInverse Problems 12 (6) 953 (1996)
https://doi.org/10.1088/0266-5611/12/6/010
Identification of transmissivity coefficients by mollification techniques. Part II: n-dimensional elliptic problems
D. HinestrozaComputers & Mathematics with Applications 30 (1) 11 (1995)
https://doi.org/10.1016/0898-1221(95)00064-6
https://doi.org/10.1002/9781118033210.ch6
Identification of the Coefficient in Elliptic Equations
Robert AcarSIAM Journal on Control and Optimization 31 (5) 1221 (1993)
https://doi.org/10.1137/0331058
Identification of transmissivity coefficients by mollification techniques. Part I: One-dimensional elliptic and parabolic problems
Doris Hinestroza and Diego A. MurioComputers & Mathematics with Applications 25 (8) 59 (1993)
https://doi.org/10.1016/0898-1221(93)90172-R
On the discretization and regularization of ill-posed problems with noncompact operators
Gennadi VainikkoNumerical Functional Analysis and Optimization 13 (3-4) 381 (1992)
https://doi.org/10.1080/01630569208816485
Theory and Practice of Geophysical Data Inversion
U. Trautenhahn and D. SchweigertTheory and Practice of Geophysical Data Inversion 3 (1992)
https://doi.org/10.1007/978-3-322-89417-5_1
Reduced SQP Methods for Parameter Identification Problems
K. Kunisch and E. W. SachsSIAM Journal on Numerical Analysis 29 (6) 1793 (1992)
https://doi.org/10.1137/0729100
Identifiability and stability of a two-parameter estimation problem1
J. Baumeister and K. KunischApplicable Analysis 40 (4) 263 (1991)
https://doi.org/10.1080/00036819108840009
13 (1990)
https://doi.org/10.1109/CDC.1990.203536
Perspectives in Control Theory
K. KunischPerspectives in Control Theory 108 (1990)
https://doi.org/10.1007/978-1-4757-2105-8_8
A new regularisation method for parameter identification in elliptic problems
U TautenhahnInverse Problems 6 (3) 465 (1990)
https://doi.org/10.1088/0266-5611/6/3/014
Estimation Techniques for Distributed Parameter Systems
H. T. Banks and K. KunischEstimation Techniques for Distributed Parameter Systems 220 (1989)
https://doi.org/10.1007/978-1-4612-3700-6_6