Local convergence of the Lavrentiev method for the Cauchy problem via a Carleman inequality

DOI10.1007/s10915-011-9571-6zbMath1280.65120OpenAlexW2040820178MaRDI QIDQ357814

Faker Ben Belgacem, Duc Thang Du, Faten Jelassi

Publication date: 13 August 2013

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-011-9571-6

zbMATH Keywords

Cauchy problemnumerical examplessuperconvergenceCarleman estimateLavrentiev regularizationbias and variance boundsdata completion problemillposedness

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Ill-posed problems for PDEs (35R25) Inverse problems for PDEs (35R30) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20) Method of contraction of the boundary for boundary value problems involving PDEs (65N45)

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Stable reconstruction of discontinuous solutions to the Cauchy problem in steady-state anisotropic heat conduction with non-smooth coefficients ⋮ Analysis of Lavrentiev-finite element methods for data completion problems ⋮ Numerical Method for Solving an Inverse Boundary Problem with Unknown Initial Conditions for Parabolic PDE Using Discrete Regularization

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