Convergence analysis for the Cauchy problem of Laplace's equation by a regularized method of fundamental solutions

DOI10.1007/s10444-009-9134-7zbMath1213.65136OpenAlexW1983630559MaRDI QIDQ609547

Ting Wei, Dayong Zhou

Publication date: 1 December 2010

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10444-009-9134-7

zbMATH Keywords

convergencecollocation methodnumerical experimentsTikhonov regularizationCauchy problem for the Laplace equationmethod of fundamental solution

Mathematics Subject Classification ID

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) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) 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 (15)

Asymptotic analysis of the conventional and invariant schemes for the method of fundamental solutions applied to potential problems in doubly-connected regions ⋮ A variational-type method of fundamental solutions for a Cauchy problem of Laplace's equation ⋮ The MFS for numerical boundary identification in two-dimensional harmonic problems ⋮ Relaxation procedures for an iterative MFS algorithm for two-dimensional steady-state isotropic heat conduction Cauchy problems ⋮ Indirect boundary integral equation method for the Cauchy problem of the Laplace equation ⋮ An inverse boundary problem for one-dimensional heat equation with a multilayer domain ⋮ Cauchy problems of Laplace's equation by the methods of fundamental solutions and particular solutions ⋮ Numerical schemes to reconstruct three-dimensional time-dependent point sources of acoustic waves ⋮ A survey of applications of the MFS to inverse problems ⋮ A regularization method for a Cauchy problem of Laplace's equation in an annular domain ⋮ An order optimal regularization method for the Cauchy problem of a Laplace equation in an annulus domain ⋮ Analysis of the dipole simulation method for two-dimensional Dirichlet problems in Jordan regions with analytic boundaries ⋮ On a general filter regularization method for the 2D and 3D Poisson equation in physical geodesy ⋮ Method of fundamental solutions for a Cauchy problem of the Laplace equation in a half-plane ⋮ On numerical approaches for solving an inverse Cauchy Stokes problem

Cites Work

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