This article is mainly concerned with the numerical study of the Cauchy problem for the Laplace equation in a bounded annular region. To solve this ill‐posed problem, we follow a variational approach based on its reformulation as a boundary control problem, for which the cost function incorporates a penalized term with the input data. The cost function is minimized by a conjugate gradient method in combination with a finite element discretization. In the case where the input data is noisy, some preliminary error estimates, show that the penalization parameter may be chosen like the inverse of the level of noise. Numerical solutions in simple and complex domains show that this methodology produces stable and accurate solutions.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1799–1822, 2017

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The main goal of this article is to study computationally the controllability of a diffusion process on the surface of a sphere in R 3 . To achieve this goal, we employ a methodology combining finite differences for the time discretization, finite elements for the space approximation, and a conjugate gradient algorithm for the iterative solution of the discrete control problems. The results of numerical experiments, obtained using the above methodology, will be presented. Furthermore, the null-controllability properties of the diffusion model under consideration will be also studied computationally.

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