FINITE-ELEMENT APPROXIMATIONS FOR THE LAPLACE OPERATOR WITH A RIGHT-HAND SIDE MEASURE

We study in this paper existence of a solution for problem Delta u = m u in fractional Sobolev spaces W-p(1+s)(Omega), s epsilon]0,1[where Om ega is an open bounded polygonal convex domain of R(2) and mu a measur e on Omega. Thanks to this regularity, we obtain estimates for del u - del u(h) and u - u(h) in L(p) norm where u(h) is the elliptic project ion on a finite element discretized space associated to the Laplace op erator.