Numerical analysis of an energy-like minimization method to solve a parabolic Cauchy problem with noisy data

Romain Rischette (1) , Thouraya Baranger (1) , Naima Debit (2)

1 LaMCoS - Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne]
2 MMCS - Modélisation mathématique, calcul scientifique

This paper is concerned with solving Cauchy problem for parabolic equation by minimizing an energy-like error functional and by taking into account noisy Cauchy data. After giving some fundamental results, numerical convergence analysis of the energy-like minimization method is carried out and leads to an adapted stopping criteria depending on noise rate for the minimization process. Numerical experiments are performed and confirm theoretical convergence order and the good behavior of the minimization process.

Mots clés: Ill-posed problem; Inverse problem; Data completion; Cauchy problem; Boundary condition identification; Noise; Finite element; A priori error estimates

Domaines: Analyse numérique [math.NA]; Thermique [physics.class-ph]; Thermique [physics.class-ph]

Romain Rischette, Thouraya Baranger, Naima Debit. Numerical analysis of an energy-like minimization method to solve a parabolic Cauchy problem with noisy data. Journal of Computational and Applied Mathematics, 2014, 271, pp.206-222. ⟨10.1016/j.cam.2014.03.024⟩. ⟨hal-00584553v3⟩