Pathological phenomena in computation of thin elastic shells

We give short account of difficulties appearing when computing thin elastic shells. <<Thin>> is understood in the sense that the ratio epsilon between the thickness and any other characteristic length of the shell is small. F or small epsilon the solution u(epsilon) itself (independently of its numer ical approximation u(h)(epsilon)) exhibits peculiarities which depend highl y on the shape and the boundary conditions of the shell. These peculiaritie s are mainly of three kinds, which do not necessarily appear simultaneously : 1) Boundary layers, 2)Global instability known as "sensitivity", 3) Const rained solutions in subspaces. The numerical approximation should be reliab le in these situations. Finite element schemes involving higher order polyn omials appear as more efficient than others. Moreover, an explicit analysis of convergence of the numerical approximation in several typical examples shows that, in order to obtain a good approximation, the mesh step must be taken smaller and smaller as epsilon decreases. Anisotropic adaptive meshes should probably be suited.