On the Alternating Method for Cauchy Problems and Its Finite Element Discretisation

DOI10.1007/978-1-4614-7816-4_11zbMath1278.65150OpenAlexW81998821MaRDI QIDQ2863542

R. Rischette, B. Tomas Johansson, Thouraya Nouri Baranger

Publication date: 22 November 2013

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

Full work available at URL: https://doi.org/10.1007/978-1-4614-7816-4_11

zbMATH Keywords

error estimatesfinite element methodCauchy problemnumerical examplesalternating methodstationary heat equationEuler-Lagrange first-order optimality equations

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Heat equation (35K05) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items (7)

Solution of nonlinear Cauchy problem for hyperelastic solids ⋮ An iterative regularizing method for an incomplete boundary data problem for the biharmonic equation ⋮ Nonlinear Cauchy problem and identification in contact mechanics: a solving method based on Bregman-gap ⋮ Boundary-integral approach to the numerical solution of the Cauchy problem for the Laplace equation ⋮ On the alternating method and boundary-domain integrals for elliptic Cauchy problems ⋮ Numerical analysis of an energy-like minimization method to solve a parabolic Cauchy problem with noisy data ⋮ Numerical solution of an elliptic 3-dimensional Cauchy problem by the alternating method and boundary integral equations

Cites Work

• Numerical analysis of an energy-like minimization method to solve the Cauchy problem with noisy data
• Constitutive law gap functionals for solving the Cauchy problem for linear elliptic PDE
• An iterative method for solving the Cauchy problem for elliptic equations
• An alternating boundary integral based method for a Cauchy problem for the Laplace equation in semi-infinite regions
• An alternating method for an inverse Cauchy problem
• On the determination of point-forces on a Stokes system
• Adaptivity with relaxation for ill-posed problems and global convergence for a coefficient inverse problem
• Relaxation procedures for an iterative algorithm for solving the Cauchy problem for the Laplace equation
• On iterative methods for solving ill-posed problems modeled by partial differential equations
• A MANN ITERATIVE REGULARIZATION METHOD FOR ELLIPTIC CAUCHY PROBLEMS
• An adaptive finite element reconstruction of distributed fluxes
• Uniqueness in the Cauchy Problem for Partial Differential Equations
• Solving Cauchy problems by minimizing an energy-like functional
• Fast reconstruction of harmonic functions from Cauchy data using integral equation techniques
• A Carleman estimate and the balancing principle in the quasi-reversibility method for solving the Cauchy problem for the Laplace equation
• Iterative methods for solving a nonlinear boundary inverse problem in glaciology
• The boundary element solution of the Cauchy steady heat conduction problem in an anisotropic medium
• An application of the reciprocity gap functional to inverse scattering theory
• Convergence of an Alternating Method to Solve the Cauchy Problem for Poisson's Equation
• A duality-based method of quasi-reversibility to solve the Cauchy problem in the presence of noisy data
• An alternating method for the stationary Stokes system
• Boundary element method for the Cauchy problem in linear elasticity.
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: On the Alternating Method for Cauchy Problems and Its Finite Element Discretisation