Estimation of a temporally and spatially varying diffusion coefficient in a parabolic system by an augmented Lagrangian technique

DOI10.1007/BF01385792zbMath0742.65090OpenAlexW2004154462MaRDI QIDQ1179037

S. Singh

Publication date: 26 June 1992

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133561

zbMATH Keywords

stabilityconvergencenumerical exampleparabolic problembiological modellingfluid flow in porous mediaaugmented Lagrangian iterative algorithmequation error methodoutput least squares methodundetermined coefficient

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Applications to the sciences (65Z05) Initial value problems for second-order parabolic equations (35K15)

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Permeability estimation of a porous structure in cancer treatment based on sampled velocity measurement* ⋮ Identification of nonlinear heat transfer laws by optimal control ⋮ A wavelet multiscale method for the inverse problem of a nonlinear convection-diffusion equation ⋮ Parameter estimation of temperature dependent material parameters in the cooling process of TMCP steel plates ⋮ Frequency domain sample maximum likelihood estimation for spatially dependent parameter estimation in PDEs ⋮ Reconstruction of a permeability field with the wavelet multiscale-homotopy method for a nonlinear convection-diffusion equation ⋮ Parameter estimation with the augmented Lagrangian method for a parabolic equation ⋮ An efficient numerical parameter estimation scheme for the space-dependent dispersion coefficient of a solute transport equation in porous media ⋮ Identification of transmissivity coefficients by mollification techniques. I: One-dimensional elliptic and parabolic problems ⋮ Identification of diffusion parameters in a nonlinear convection-diffusion equation using the augmented Lagrangian method ⋮ Identification of space-dependent permeability in nonlinear diffusion equation from interior measurements using wavelet multiscale method ⋮ SQP methods for parameter identification problems arising in hyperthermia ⋮ An adaptive homotopy method for permeability estimation of a nonlinear diffusion equation

Cites Work

• The augmented Lagrangian method for equality and inequality constraints in Hilbert spaces
• Modeling insect dispersal and estimating parameters when mark-release techniques may cause initial disturbances
• Output least squares stability in elliptic systems
• A Numerical Study of an Augmented Lagrangian Method for the Estimation of Parameters in Elliptic Systems
• Convergence rates for Tikhonov regularisation of non-linear ill-posed problems
• The Augmented Lagrangian Method for Parameter Estimation in Elliptic Systems
• Estimation of variable coefficients in parabolic distributed systems
• First and second-order necessary and sufficient optimality conditions for infinite-dimensional programming problems
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