A regularization method for a Cauchy problem of Laplace's equation in an annular domain

DOI10.1016/j.matcom.2012.05.009zbMath1259.65138OpenAlexW2000427788MaRDI QIDQ1761660

Xianqiang Yang

Publication date: 15 November 2012

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matcom.2012.05.009

zbMATH Keywords

convergenceCauchy problemLaplace equationTikhonov regularizationmethod of fundamental solutions

Mathematics Subject Classification ID

Ill-posed problems for PDEs (35R25) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs (65M30) Fundamental solutions, Green's function methods, etc. for initial value and initial-boundary value problems involving PDEs (65M80)

Related Items

Method for recovering boundary data in a two-dimensional Poisson equation on annular domain, Numerical solution of continuation problem for 3D steady-state diffusion in cylindrically layered medium, Numerical solutions of 3D Cauchy problems of elliptic operators in cylindrical domain using local weak equations and radial basis functions, A new filtering method for the Cauchy problem of the Laplace equation, On a general filter regularization method for the 2D and 3D Poisson equation in physical geodesy, An optimal quasi solution for the Cauchy problem for Laplace equation in the framework of inverse ECG

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Convergence analysis for the Cauchy problem of Laplace's equation by a regularized method of fundamental solutions
• The method of fundamental solutions for inverse boundary value problems associated with the two-dimensional biharmonic equation
• Stability analysis of method of fundamental solutions for mixed boundary value problems of Laplace's equation
• The method of fundamental solutions for annular shaped domains
• Asymptotic stability of the fundamental solution method
• Charge simulation method using exterior mapping functions
• Some aspects of the method of fundamental solutions for certain harmonic problems
• Uniqueness and convergence of numerical solution of the Cauchy problem for the Laplace equation by a charge simulation method
• The collocation points of the fundamental solution method for the potential problem
• The MFS for numerical boundary identification in two-dimensional harmonic problems
• Method of fundamental solutions with regularization techniques for Cauchy problems of elliptic operators
• A meshless method for some inverse problems associated with the Helmholtz equation
• Backus-Gilbert algorithm for the Cauchy problem of the Laplace equation
• Numerical solution of a Cauchy problem for the Laplace equation
• Numerical Computation of a Cauchy Problem for Laplace's Equation
• Extended-domain-Lavrentiev's regularization for the Cauchy problem
• The Lavrentiev regularization of the data completion problem
• A Carleman estimate and the balancing principle in the quasi-reversibility method for solving the Cauchy problem for the Laplace equation
• Fundamental Solutions Method for Elliptic Boundary Value Problems
• Logarithmic Convexity for Discrete Harmonic Functions and the Approximation of the Cauchy Problem for Poisson's Equation
• A Computational Quasi-Reversibility Method for Cauchy Problems for Laplace’s Equation
• Stability and Regularization of a Discrete Approximation to the Cauchy Problem for Laplace's Equation
• Computation for MultiDimensional Cauchy Problem
• Stable determination of corrosion by a single electrostatic boundary measurement
• One new strategy for a priori choice of regularizing parameters in Tikhonov's regularization
• The Cauchy problem for Laplace's equation via the conjugate gradient method
• L2-Conditional stability estimate for the Cauchy problem for the Laplace equation
• The method of fundamental solutions for solving a Cauchy problem of Laplace's equation in a multi-connected domain
• Tikhonov Regularization by a Reproducing Kernel Hilbert Space for the Cauchy Problem for an Elliptic Equation
• Convergence rates for the quasi-reversibility method to solve the Cauchy problem for Laplace's equation
• An Energy Regularization for Cauchy Problems of Laplace Equation in Annulus Domain
• A mixed formulation of quasi-reversibility to solve the Cauchy problem for Laplace's equation
• Numerical analysis of the method of fundamental solution for harmonic problems in annular domains