S Andrieux et al 2006 Inverse Problems 22 115 doi:10.1088/0266-5611/22/1/007
S Andrieux1, T N Baranger2 and A Ben Abda3
Show affiliationsAn energy-like error functional is introduced in the context of the ill-posed problem of boundary data recovering, which is well known as a Cauchy problem. Links with existing methods for data completion are detailed. Here the problem is converted into an optimization problem; the computation of the gradients of the energy-like functional is given for both the continuous and the discrete problems. Numerical experiments highlight the efficiency of the proposed method as well as its robustness in the model context of Laplace's equation, but also for anisotropic conductivity problems.
02.30.Jr Partial differential equations
02.60.Lj Ordinary and partial differential equations; boundary value problems
83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)
35J05 Laplace equation, reduced wave equation (Helmholtz), Poisson equation (See also 31Axx, 31Bxx)
Issue 1 (February 2006)
Received 18 August 2005, in final form 22 November 2005
Published 13 January 2006
S Andrieux et al 2006 Inverse Problems 22 115
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