Etude de la solution approchée de problèmes quasilinéaires et analyse d'un problème en théorie du signal

Abstract : In the first part of this work, we complete the results obtained by N. André and M. Chipot about the approximate solution of some class of elliptic problems, by using the simplest finite element method. In particular, in two dimensional case, we present a new technique to prove uniqueness for the approximate solution when the mesh size approaches zero, under optimal assumptions about the angles of the triangulation. Moreover, we studied the discrete maximum principle, the convergence, the regularity and the uniqueness in higher dimension. In the second part, we are interested in an industrial problem suggested by Landis & Gyr energy management. This problem consist of finding a numerical technique to measure the energy of an electrical signal
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Mohamed Amrani. Etude de la solution approchée de problèmes quasilinéaires et analyse d'un problème en théorie du signal. Mathématiques générales [math.GM]. Université Paul Verlaine - Metz, 1995. Français. ⟨NNT : 1995METZ035S⟩. ⟨tel-01777091⟩

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