Solving Cauchy problems by minimizing an energy-like functional

被引:152
作者
Andrieux, S [1 ]
Baranger, TN
Ben Abda, A
机构
[1] CNRS, UMR 2832, LaMSID, EDF, Clamart, France
[2] Univ Lyon 1, Ctr Mecan, F-69365 Lyon, France
关键词
D O I
10.1088/0266-5611/22/1/007
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
An 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.
引用
收藏
页码:115 / 133
页数:19
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