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A convergent adaptive finite element method for electrical impedance tomography

https://doi.org/10.1093/imanum/drw045
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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1002/047134608x.w1431.pub2openalex-snapshot
Electrical Impedance Tomography
inferredcites →https://doi.org/10.1002/9781118032824openalex-snapshot
A Posteriori Error Estimation in Finite Element Analysis
inferredcites →https://doi.org/10.1002/nme.3247openalex-snapshot
A reconstruction algorithm for electrical impedance tomography based on sparsity regularization
inferredcites →https://doi.org/10.1007/978-0-387-92920-0_14openalex-snapshot
Electrical Impedance Tomography
inferredcites →https://doi.org/10.1007/978-3-642-03413-8_12openalex-snapshot
Theory of adaptive finite element methods: An introduction
inferredcites →https://doi.org/10.1007/s00211-003-0482-9openalex-snapshot
A posteriori error estimation for finite element discretization of parameter identification problems
inferredcites →https://doi.org/10.1007/s10444-007-9035-6openalex-snapshot
Adaptive finite element methods for the identification of distributed parameters in elliptic equation
inferredcites →https://doi.org/10.1007/s10958-010-9921-1openalex-snapshot
Adaptivity with relaxation for ill-posed problems and global convergence for a coefficient inverse problem
inferredcites →https://doi.org/10.1016/0377-0427(94)90034-5openalex-snapshot
A recursive approach to local mesh refinement in two and three dimensions
inferredcites →https://doi.org/10.1016/j.camwa.2013.12.003openalex-snapshot
Axioms of adaptivity
inferredcites →https://doi.org/10.1016/j.jcp.2013.12.010openalex-snapshot
Expectation propagation for nonlinear inverse problems – with an application to electrical impedance tomography
inferredcites →https://doi.org/10.1016/s0045-7825(96)01107-3openalex-snapshot
A posteriori error estimation in finite element analysis
inferredcites →https://doi.org/10.1016/s0168-2024(08)x7014-6openalex-snapshot
The Finite Element Method for Elliptic Problems
inferredcites →https://doi.org/10.1023/a:1014239012739openalex-snapshot
A Posteriori Error Estimates for Distributed Convex Optimal Control Problems
inferredcites →https://doi.org/10.1051/cocv/2011193openalex-snapshot
An analysis of electrical impedance tomography with applications to Tikhonov regularization
inferredcites →https://doi.org/10.1051/cocv:2007057openalex-snapshot
Ana posteriorierror analysis of adaptive finite element methods for distributed elliptic control problems with control constraints
inferredcites →https://doi.org/10.1088/0266-5611/22/6/004openalex-snapshot
Newton regularizations for impedance tomography: a numerical study
inferredcites →https://doi.org/10.1088/0266-5611/24/2/025025openalex-snapshot
Efficient computation of the Tikhonov regularization parameter by goal-oriented adaptive discretization
inferredcites →https://doi.org/10.1088/0266-5611/26/12/125009openalex-snapshot
Reconstruction of dielectrics from experimental data via a hybrid globally convergent/adaptive inverse algorithm
inferredcites →https://doi.org/10.1088/0266-5611/26/4/045012openalex-snapshot
A posteriori error estimates for the adaptivity technique for the Tikhonov functional and global convergence for a coefficient inverse problem
inferredcites →https://doi.org/10.1088/0266-5611/27/7/075009openalex-snapshot
An adaptive finite element reconstruction of distributed fluxes
inferredcites →https://doi.org/10.1088/0266-5611/28/12/123001openalex-snapshot
Sparsity regularization for parameter identification problems
inferredcites →https://doi.org/10.1088/0266-5611/30/4/045013openalex-snapshot
An analysis of finite element approximation in electrical impedance tomography
inferredcites →https://doi.org/10.1088/0266-5611/30/9/095003openalex-snapshot
A direct sampling method for electrical impedance tomography
inferredcites →https://doi.org/10.1090/mcom/2961openalex-snapshot
Convergence of an adaptive finite element method for distributed flux reconstruction
inferredcites →https://doi.org/10.1090/s0025-5718-1990-1011446-7openalex-snapshot
Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
inferredcites →https://doi.org/10.1093/imanum/drq001openalex-snapshot
A convergence proof for adaptive finite elements without lower bound
inferredcites →https://doi.org/10.1109/10.35300openalex-snapshot
Electrode models for electric current computed tomography
inferredcites →https://doi.org/10.1115/1.3424474openalex-snapshot
The Finite Element Method for Elliptic Problems
inferredcites →https://doi.org/10.1137/0152060openalex-snapshot
Existence and Uniqueness for Electrode Models for Electric Current Computed Tomography
inferredcites →https://doi.org/10.1137/050631252openalex-snapshot
An Adaptive Hybrid FEM/FDM Method for an Inverse Scattering Problem in Scanning Acoustic Microscopy
inferredcites →https://doi.org/10.1137/070683295openalex-snapshot
The Factorization Method Applied to the Complete Electrode Model of Impedance Tomography
inferredcites →https://doi.org/10.1137/090761823openalex-snapshot
Goal-Oriented Adaptivity in Pointwise State Constrained Optimal Control of Partial Differential Equations
inferredcites →https://doi.org/10.1137/1.9780898718614openalex-snapshot
Lagrange Multiplier Approach to Variational Problems and Applications
inferredcites →https://doi.org/10.1137/1.9781611972030openalex-snapshot
Elliptic Problems in Nonsmooth Domains
inferredcites →https://doi.org/10.1137/120886984openalex-snapshot
Monotonicity-Based Shape Reconstruction in Electrical Impedance Tomography
inferredcites →https://doi.org/10.1137/130941742openalex-snapshot
Analysis of an Adaptive Finite Element Method for Recovering the Robin Coefficient
inferredcites →https://doi.org/10.1137/140958955openalex-snapshot
Resolution-Controlled Conductivity Discretization in Electrical Impedance Tomography
inferredcites →https://doi.org/10.1137/s0363012901389342openalex-snapshot
Adaptive Finite Element Approximation for Distributed Elliptic Optimal Control Problems
inferredcites →https://doi.org/10.1142/9120#t=tocopenalex-snapshot
Inverse Problems: Tikhonov Theory And Algorithms
inferredcites →https://doi.org/10.1142/s0218202505003885openalex-snapshot
A POSTERIORI ERROR ESTIMATION IN COMPUTATIONAL INVERSE SCATTERING
inferredcites →https://doi.org/10.1145/76909.76912openalex-snapshot
A comparison of adaptive refinement techniques for elliptic problems
inferredcites →https://doi.org/10.1201/9780203747940openalex-snapshot
Measure Theory and Fine Properties of Functions
inferredcites →https://doi.org/10.2478/cmam-2011-0006openalex-snapshot
Quasi-optimality of an Adaptive Finite Element Method for an Optimal Control Problem
inferredcites →https://doi.org/10.3934/ipi.2009.3.599openalex-snapshot
Regularized D-bar method for the inverse conductivity problem
inferredcites →https://doi.org/10.3934/ipi.2016030openalex-snapshot
The Bayesian formulation of EIT: Analysis and algorithms

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

inferred← citeshttps://doi.org/10.2139/ssrn.4670598openalex-extracted
Discontinuous Galerkin Method for Electrical Impedance Tomography with Partial Data
inferred← citeshttps://doi.org/10.1007/978-3-030-48634-1_5openalex-snapshot
Regularized Linear Inversion with Randomized Singular Value Decomposition
inferred← citeshttps://doi.org/10.1016/bs.hna.2025.09.003openalex-snapshot
Deep learning based reconstruction methods for electrical impedance tomography
inferred← citeshttps://doi.org/10.1016/j.cam.2023.115344openalex-snapshot
A high order discontinuous Galerkin method for the recovery of the conductivity in Electrical Impedance Tomography
inferred← citeshttps://doi.org/10.1016/j.cam.2024.116376openalex-snapshot
An analysis of discontinuous Galerkin method for Electrical Impedance Tomography with partial data
inferred← citeshttps://doi.org/10.1016/j.cam.2025.116488openalex-snapshot
Numerical shape reconstruction approaches for solving free boundary inverse problem for the p -Laplacian operator
inferred← citeshttps://doi.org/10.1016/j.jcp.2019.109123openalex-snapshot
Recovering elastic inclusions by shape optimization methods with immersed finite elements
inferred← citeshttps://doi.org/10.1038/s41598-025-15543-2openalex-snapshot
Use of an anatomical atlas in real-time EIT reconstructions of ventilation and pulsatile perfusion in preterm infants
inferred← citeshttps://doi.org/10.1088/1361-6420/ac4f5copenalex-snapshot
Optimal convergence of finite element approximation to an optimization problem with PDE constraint*
inferred← citeshttps://doi.org/10.1088/1361-6420/adf255openalex-snapshot
Multi-scale frequency-enhanced deep D-bar method for electrical impedance tomography
inferred← citeshttps://doi.org/10.1088/2399-6528/aad976openalex-snapshot
Convergence of finite element approximation for electrical impedance tomography with the complete electrode model
inferred← citeshttps://doi.org/10.1090/conm/784/15750openalex-snapshot
Discretization and Convergence of the EIT Optimal Control Problem in 2D and 3D Domains
inferred← citeshttps://doi.org/10.1109/tbme.2021.3105056openalex-snapshot
An Efficient Point-Matching Method-of-Moments for 2D and 3D Electrical Impedance Tomography Using Radial Basis Functions
inferred← citeshttps://doi.org/10.1109/tci.2026.3723134openalex-snapshot
Cross-Scale Neural Representation for Electrical Impedance Tomography
inferred← citeshttps://doi.org/10.1109/tim.2023.3301859openalex-snapshot
FFT-Accelerated Transformation-Domain Image Reconstruction for Electrical Impedance Tomography
inferred← citeshttps://doi.org/10.1137/20m1367350openalex-snapshot
Construct Deep Neural Networks based on Direct Sampling Methods for Solving Electrical Impedance Tomography
inferred← citeshttps://doi.org/10.1515/jiip-2017-0067openalex-snapshot
Convexification of restricted Dirichlet-to-Neumann map
inferred← citeshttps://doi.org/10.17268/sel.mat.2023.01.09openalex-snapshot
Applications of the duality theory of convex analysis to the complete electrode model of electrical impedance tomography
inferred← citeshttps://doi.org/10.2139/ssrn.5449648openalex-snapshot
Solver-in-the-Loop joint operator learning: fractional Laplace-Beltrami features for interface reconstruction
inferred← citeshttps://doi.org/10.32657/10356/173918openalex-snapshot
Some approximation methods for Bayesian inversion of electrical impedance tomography
inferred← citeshttps://doi.org/10.3934/ipi.2020074openalex-snapshot
Some application examples of minimization based formulations of inverse problems and their regularization
inferred← citeshttps://doi.org/10.3934/mbe.2021246openalex-snapshot
Cancer detection through Electrical Impedance Tomography and optimal control theory: theoretical and computational analysis
inferred← citeshttps://doi.org/10.4208/eajam.2023-075.010623openalex-snapshot
Numerical Shape Reconstruction for a Semi-Linear Elliptic Interface Inverse Problem
inferred← citeshttps://doi.org/10.48550/arxiv.2009.03384openalex-snapshot
Discretization and Convergence of the EIT Optimal Control Problem in 2D and 3D Domains
inferred← citeshttps://doi.org/10.48550/arxiv.2011.04991openalex-snapshot
Weak Galerkin Method for Electrical Impedance Tomography
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