Abstract
An energy error functional is introduced in the context of the ill-posed problem of boundary data recovery in linear elasticity, which is well known as the Cauchy problem. The problem is converted into one of optimization; the computation of the gradients of the energy functional is given for both the continuous and the discrete problems. Links with existing methods for data completion are described and numerical experiments highlight the efficiency of the proposed method as well as its robustness in the case of singular data.
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Baranger, T.N., Andrieux, S. An optimization approach for the Cauchy problem in linear elasticity. Struct Multidisc Optim 35, 141–152 (2008). https://doi.org/10.1007/s00158-007-0123-5
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DOI: https://doi.org/10.1007/s00158-007-0123-5