Solving a Cauchy problem for a 3D elliptic PDE with variable coefficients by a quasi-boundary-value method

DOI10.1088/0266-5611/30/1/015005zbMath1292.65111OpenAlexW2084406730MaRDI QIDQ5406748

Lars Eldén, Xiao-Li Feng

Publication date: 2 April 2014

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-103280

zbMATH Keywords

finite difference methodCauchy problemfast Fourier transformthree dimensionselliptic equationvariable coefficientsill-posedfast solverleft-preconditioned GMRESquasi-boundary-value method

Mathematics Subject Classification ID

Ill-posedness and regularization problems in numerical linear algebra (65F22) Iterative numerical methods for linear systems (65F10) Numerical methods for discrete and fast Fourier transforms (65T50) Finite difference methods for boundary value problems involving PDEs (65N06) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20)

Related Items (13)

Unknown source identification problem for space-time fractional diffusion equation: optimal error bound analysis and regularization method ⋮ Cauchy problem for the Laplace equation in a radially symmetric hollow cylinder ⋮ Regularization method for an ill-posed Cauchy problem for elliptic equations ⋮ On stochastic elliptic equations driven by Wiener process with non-local condition ⋮ Uniqueness' failure for the finite element Cauchy-Poisson's problem ⋮ Analysis of Lavrentiev-finite element methods for data completion problems ⋮ Artificial neural network approximations of Cauchy inverse problem for linear PDEs ⋮ A modified quasi-boundary value method for a two-dimensional inverse heat conduction problem ⋮ On an inverse boundary value problem of a nonlinear elliptic equation in three dimensions ⋮ The quasi-boundary value method for identifying the initial value of heat equation on a columnar symmetric domain ⋮ Full Discretization of Cauchy's Problem by Lavrentiev--Finite Element Method ⋮ A potential-free field inverse Schrödinger problem: optimal error bound analysis and regularization method ⋮ \textit{A posteriori} regularization method for the two-dimensional inverse heat conduction problem

This page was built for publication: Solving a Cauchy problem for a 3D elliptic PDE with variable coefficients by a quasi-boundary-value method