Stability analysis of the Fourier–Bessel method for the Cauchy problem of the Helmholtz equation

DOI10.1080/17415977.2015.1051531zbMath1398.65323OpenAlexW1497214897MaRDI QIDQ3177934

Deyue Zhang, Wei Sun

Publication date: 8 July 2016

Published in: Inverse Problems in Science and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17415977.2015.1051531

zbMATH Keywords

stability analysisCauchy problemsCarleman estimateimproperly posed problemsFourier-Bessel method

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Ill-posed problems for PDEs (35R25) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20)

Related Items (5)

Solving the Cauchy problem for the Helmholtz equation using cubic smoothing splines ⋮ Analysis of Dirichlet-Robin iterations for solving the Cauchy problem for elliptic equations ⋮ A direct imaging method for the exterior and interior inverse scattering problems ⋮ The Fourier–Bessel method for the inverse scattering problem of cavities ⋮ A Fourier-Bessel method with a regularization strategy for the boundary value problems of the Helmholtz equation

Cites Work

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• Carleman estimates for global uniqueness, stability and numerical methods for coefficient inverse problems
• Boundary particle method for Cauchy inhomogeneous potential problems
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• Numerical solution of an inverse 2D Cauchy problem connected with the Helmholtz equation
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• A duality-based method of quasi-reversibility to solve the Cauchy problem in the presence of noisy data
• An introduction to the mathematical theory of inverse problems

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