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On analyse des approximations par elements finis des solutions irregulieres des problemes aux limites et aux conditions initiales pour les equations hyperboliques de second ordre. Pour des schemas de semi-discretisation et de discretisation totale, on obtient des majorations de l'erreur par rapport a des normes d'ordre negatif. Ces schemas utilisent la projection L 2 de la valeur initiale qui est dans L 2

Semidiscrete and single step fully discrete finite element approximations for second order hyperbolic equations with nonsmooth solutions