The Cauchy problem for Laplace’s equation via the conjugate gradient method

By D. Hào, Daniel Lesnic. 2000

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Conjugate gradient-boundary element solution to the Cauchy problem for Helmholtz-type equations (2003, methodology): “Although not illustrated here, an important conclusion is reported, namely that the numerical solution for the temperature TjC1 is more accurate for the Cauchy problem in an annulus, i.e. examples 1 and 2, than for the Cauchy problem in a disk, see e.g. Hào and Lesnic [23] and Marin et al. [24].”
Conjugate gradient method for the Robin inverse problem associated with the Laplace equation (2007, unknown): “Each iteration of the algorithm requires solving three well-posed problems: the direct problem (4); the adjoint problem (12) and the sensitivity problem (11), which is one more than that for the Cauchy problem [26].”