A mixed formulation of quasi-reversibility to solve the Cauchy problem for Laplace's equation

Laurent Bourgeois 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : This work concerns the use of the method of quasi-reversibility to solve the Cauchy problem for Laplace's equation. We describe a mixed formulation of the method and its relationship with a classical formulation. A discretized formulation using finite elements of class C0 is derived from the mixed formulation, and convergence of the solution of this discretized problem with noisy data to the exact solution is analysed. Finally, a simple numerical example is implemented in order to show the feasibility of the method. © 2005 IOP Publishing Ltd.
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Journal articles
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Laurent Bourgeois. A mixed formulation of quasi-reversibility to solve the Cauchy problem for Laplace's equation. Inverse Problems, IOP Publishing, 2005, 21 (3), pp.1087-1104. ⟨10.1088/0266-5611/21/3/018⟩. ⟨hal-00876244⟩

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