An approximate solution of differential inclusion with prox-regular set

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Abstract The aim of this paper is to calculate the approximate solution of differential inclusion with prox-regular set, the question is how to calculate this solution? We use the discrete approximation property of a new variant of nonconvex sweeping processes involving normal cone and a finite element method. Knowing that the majority of mathematicians have proved only the existence and uniqueness of the solution for this type of inclusions, like: Mordukhovich, Thibault, Aubin, Messaoud,...etc. MSC Classification: 34A60 , 49J52 , 37B25.

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