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This paper is devoted to the analysis of a numerical scheme based on theFinite Element Method for approximating the solution of Koiter's model for alinearly elastic elliptic membrane shell subjected to remaining confined in aprescribed half-space. First, we show that the solution of the obstacle problemunder consideration is uniquely determined and satisfies a set of variationalinequalities which are governed by a fourth order elliptic operator, and whichare posed over a non-empty, closed, and convex subset of a suitable space.Second, we show that the solution of the obstacle problem under considerationcan be approximated by means of the penalty method. Third, we show that thesolution of the corresponding penalised problem is more regular up to theboundary. Fourth, we write down the mixed variational formulation correspondingto the penalised problem under consideration, and we show that the solution ofthe mixed variational formulation is more regular up to the boundary as well.In view of this result concerning the augmentation of the regularity of thesolution of the mixed penalised problem, we are able to approximate thesolution of the one such problem by means of a Finite Element scheme. Finally,we present numerical experiments corroborating the validity of the mathematicalresults we obtained.

Numerical approximation of the solution of Koiter's model for an elliptic membrane shell subjected to an obstacle via the penalty method