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Formulation variationnelle pour le calcul de la diffraction d’une onde acoustique par une surface rigide. (Variational formulation for the computation of the diffraction of an acoustic wave by a rigid surface). (French) Zbl 0636.65119
The authors consider a numerical technique for solving the Neumann problem in time dependent acoustic scattering. They proved in a foregoing paper [ibid. 8, 405-435 (1986; Zbl 0618.35069)] existence and uniqueness in Sobolev spaces using double layer retarded potentials. Here a variational formulation of the problem is given and a semi-discrete method of Galerkin type for its numerical approximation is considered which then is discretized with respect to time. Stability and convergence results complete the paper.
Reviewer: A.Kirsch

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N40 Method of lines for boundary value problems involving PDEs
35L05 Wave equation
76Q05 Hydro- and aero-acoustics
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References:
[1] Bamberger, Formulation Variationnelle Espace-Temps pour le Calcul par potentiel Retardé de la Diffraction d’une onde acoustic (I). Math. Meth. in the Appl, Sci. 8 pp 405– (1986) · Zbl 0618.35069
[2] Bendali , A. Approximation par éléments finis de surface de problèmes de diffraction des ondes électromagnétiques. 1984
[3] Hamdi, Une formulation variationnelle par équations intégrales pour la résolution de l’équation de Helmholtz avec des conditions aux limites mixtes, CRAS, série II 292 pp 17– (1981)
[4] Nedelec , J. C. Approximation des équations intégrales en mécanique et en physique. Cours de l’Ecole d’Eté d’Analyse Numérique EDF-CEA-INRIA 1977
[5] Nedelec, Approximation par potentiel de double couche du problème de Neumann extérieur, CRAS, série A 286 pp 616– (1977)
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