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

This paper is concerned with solving the Cauchy problem for the 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 the theoretical convergence order and the good behavior of the minimization process.