Matrix coefficient identification in an elliptic equation with the convex energy functional method

DOI10.1088/0266-5611/32/8/085007zbMath1353.65115arXiv1510.05489OpenAlexW2218814789MaRDI QIDQ2820676

Michael Hinze, Tran Nhan Tam Quyen

Publication date: 9 September 2016

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.05489

zbMATH Keywords

inverse problemfinite element methodnumerical experimentsconvergence rateTikhonov regularizationelliptic equationH-convergencediffusion matrixsource conditiongradient-projection algorithmcoefficient identificationconvex energy function

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Inverse problems for PDEs (35R30) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21)

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Identification of matrix diffusion coefficient in a parabolic PDE ⋮ Parameter identification for heterogeneous materials by optimal control approach with flux cost functionals ⋮ Variational method for multiple parameter identification in elliptic PDEs ⋮ Heuristic discrepancy principle for variational regularization of inverse problems ⋮ Finite element approximation of source term identification with TV-regularization ⋮ An ADMM-Newton-CNN numerical approach to a TV model for identifying discontinuous diffusion coefficients in elliptic equations: convex case with gradient observations

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