A numerical study of variable coefficient elliptic Cauchy problem via projection method

DOI10.1080/00207160.2012.659426zbMath1255.65083OpenAlexW1974020979MaRDI QIDQ4903575

Hari Shanker Gupta

Publication date: 22 January 2013

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160.2012.659426

zbMATH Keywords

inverse problemelliptic partial differential equationsregularization methodill-posed problemsbalancing principleellitic Cauchy problem

Mathematics Subject Classification ID

Ill-posedness and regularization problems in numerical linear algebra (65F22) Inverse problems for PDEs (35R30) Linear operators and ill-posed problems, regularization (47A52) Numerical solution to inverse problems in abstract spaces (65J22)

Related Items (1)

Modified method of fundamental solutions for the Cauchy problem connected with the Laplace equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Regularisierung schlecht gestellter Probleme durch Projektionsverfahren
• Nonconvergence results for the application of least-squares estimation to ill-posed problems
• Regularity of an elliptic problem with mixed Dirichlet-Robin boundary conditions in a polygonal domain
• Numerical method for solving a class of nonlinear elliptic inverse problems.
• On the balancing principle for some problems of numerical analysis
• Formulation of the problem of sonic boom by a maneuvering aerofoil as a one-parameter family of Cauchy problems
• Mean value iterations for nonlinear elliptic Cauchy problems
• Backus-Gilbert algorithm for the Cauchy problem of the Laplace equation
• Solution of the Cauchy problem using iterated Tikhonov regularization
• A MANN ITERATIVE REGULARIZATION METHOD FOR ELLIPTIC CAUCHY PROBLEMS
• Solving Cauchy problems by minimizing an energy-like functional
• Why is the Cauchy problem severely ill-posed?
• A Carleman estimate and the balancing principle in the quasi-reversibility method for solving the Cauchy problem for the Laplace equation
• Determining conductivity by boundary measurements II. Interior results
• An inverse Robin problem for Laplace's equation: theoretical results and numerical methods
• The Cauchy problem for Laplace's equation via the conjugate gradient method
• Regularization by projection with a posteriori discretization level choice for linear and nonlinear ill-posed problems
• Self-regularization of projection methods with a posteriori discretization level choice for severely ill-posed problems
• Reconstruction of boundary data for a class of nonlinear inverse problems
• A duality-based method of quasi-reversibility to solve the Cauchy problem in the presence of noisy data
• Tikhonov Regularization by a Reproducing Kernel Hilbert Space for the Cauchy Problem for an Elliptic Equation
• The balancing principle for the regularization of elliptic Cauchy problems
• On the Adaptive Selection of the Parameter in Regularization of Ill-Posed Problems
• On Cauchy's problem: II. Completion, regularization and approximation
• Inverse problems for partial differential equations

This page was built for publication: A numerical study of variable coefficient elliptic Cauchy problem via projection method