Simultaneous reconstruction of the solution and the source of hyperbolic equations from boundary measurements: a robust numerical approach

DOI10.1088/0266-5611/32/11/115020zbMath1414.65017arXiv1505.02566OpenAlexW2536173731MaRDI QIDQ2835455

Publication date: 2 December 2016

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

Full work available at URL: https://arxiv.org/abs/1505.02566

zbMATH Keywords

wave equation inverse problems finite element discretization optimality condition mixed formulation

Mathematics Subject Classification ID

Sensitivity, stability, well-posedness (49K40) Optimality conditions for problems involving partial differential equations (49K20) Inverse problems for PDEs (35R30) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Discrete approximations in optimal control (49M25) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32)

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Inverse problems for linear parabolic equations using mixed formulations. Part 1: Theoretical analysis ⋮ An application of moment method to uniform boundary controllability property of a semidiscrete 1-d wave equation with a lower rate vanishing viscosity ⋮ Fully discrete finite element data assimilation method for the heat equation ⋮ Preconditioning inverse problems for hyperbolic equations with applications to photoacoustic tomography ⋮ Approximation of the controls for the wave equation with a potential ⋮ Reconstruction of initial wave with radiation boundary condition via boundary sensing

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