R6sum6. On commence en posant un probl6me d'6volution avec contraintes unilat6rales, d6pendantes du temps, pour lequel on donne deux th6or~mes de r6gularit6.On fait ensuite l'approximation num6rique par la m6thode des 616ments finis et on montre un algorithme de r6solution pour les syst6mes de compl6mentarit6 associ6s aux probl~mes approch6s.On obtient enfin une majoration de l'erreur d'approximation.
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