Adaptive finite element method for a coefficient inverse problem for Maxwell's system

DOI10.1080/00036811.2010.502116zbMath1223.78010OpenAlexW2162275309WikidataQ58123921 ScholiaQ58123921MaRDI QIDQ3094241

Larisa Beilina

Publication date: 21 October 2011

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036811.2010.502116

zbMATH Keywords

adaptive finite element methods\(a\) posteriori error estimationtime-dependent inverse electromagnetic scattering

Mathematics Subject Classification ID

Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) Inverse problems (including inverse scattering) in optics and electromagnetic theory (78A46)

Related Items (12)

An adaptive finite element method in reconstruction of coefficients in Maxwell's equations from limited observations. ⋮ Numerical resolution of an electromagnetic inverse medium problem at fixed frequency ⋮ Time-adaptive determination of drug efficacy in mathematical model of HIV infection ⋮ Lipschitz stability for an inverse hyperbolic problem of determining two coefficients by a finite number of observations ⋮ Relaxation property for the adaptivity for ill-posed problems ⋮ Optimization approach for the simultaneous reconstruction of the dielectric permittivity and magnetic permeability functions from limited observations ⋮ Sensitivity analysis for 3D Maxwell's equations and its use in the resolution of an inverse medium problem at fixed frequency ⋮ Determination of Permittivity from Propagation Constant Measurements in Optical Fibers ⋮ Time-adaptive FEM for distributed parameter identification in mathematical model of HIV infection with drug therapy ⋮ Time-Adaptive FEM for Distributed Parameter Identification in Biological Models ⋮ Adaptive FEM with Relaxation for a Hyperbolic Coefficient Inverse Problem ⋮ Globally convergent and adaptive finite element methods in imaging of buried objects from experimental backscattering radar measurements

Uses Software

• L-BFGS

Cites Work

• A new family of mixed finite elements in \({\mathbb{R}}^ 3\)
• A mixed finite element formulation for Maxwell's equations in the time domain
• A posteriori estimates for partial differential equations
• Adaptivity with relaxation for ill-posed problems and global convergence for a coefficient inverse problem
• A posteriori error estimates for the adaptivity technique for the Tikhonov functional and global convergence for a coefficient inverse problem
• Éléments finis d'arête et condensation de masse pour les équations de Maxwell: le cas 2D
• A POSTERIORI ERROR ESTIMATION IN COMPUTATIONAL INVERSE SCATTERING
• Finite Element Methods for Maxwell's Equations
• An Adaptive Hybrid FEM/FDM Method for an Inverse Scattering Problem in Scanning Acoustic Microscopy

This page was built for publication: Adaptive finite element method for a coefficient inverse problem for Maxwell's system