Central difference regularization method for inverse source problem on the Poisson equation

DOI10.1080/17476933.2014.940926zbMath1322.65100OpenAlexW2143885540MaRDI QIDQ4982012

Songshu Liu, Jingjun Zhao

Publication date: 23 March 2015

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17476933.2014.940926

zbMATH Keywords

stabilityerror estimatePoisson equationinverse source problemnumerical resultmollification methodcentral difference regularization method

Mathematics Subject Classification ID

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) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Finite difference methods for boundary value problems involving PDEs (65N06) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21)

Cites Work

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• A multi-frequency inverse source problem
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• The boundary-element method for the determination of a heat source dependent on one variable
• Two numerical methods for solving a backward heat conduction problem
• The method of fundamental solutions for inverse source problems associated with the steady-state heat conduction
• A projective method for an inverse source problem of the Poisson equation
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• Numerical solution of the sideways heat equation by difference approximation in time
• The inverse source problem for Maxwell's equations
• Identification of source locations in two-dimensional heat equations
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