Istituto di Matematica Applicata e Tecnologie Informatiche     
Boffi D., Chinosi C., Gastaldi L. Approximation of grad-div operator in non-convex domains. Preprint ercim.cnr.ian//1999-1136, 1999.
In this paper we are dealing with the approximation of the grad-div operator in non-convex polygonal domains. A penalization strategy is considered in order to obtain a formulation of the original eigenproblem which is associated with an elliptic operator. However the presence of singular eigensolutions, in the case of non-convex domains, is the origin of major troubles in the numerical approximation of the problem. A mixed-type approximation, based on an under-integrated scheme, is introduced and analyzed from the theoretical and numerical point of view. Several numerical experiments confirm that in presence of singularities the under-integrated scheme is needed in order to reproduce the feautures of the continuous problem.
Subject Finite element method, non-convex domain, eigenvalue problem, corner singularities, fluid-structure interaction
65N30, 65Dxx

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