Singularities in shell theory: Anisotropic error estimates and numerical simulations

In this paper, we show the efficiency of anisotropic adaptive meshes in the computation of very thin shell problems including boundary and internal layers phenomena. In a first part, we present general results concerning the structure of the singularities appearing inside these layers which depends on the geometrical nature of the shell. Then, we establish error estimates which reveal the performance and the efficiency of using anisotropic and adapted meshes inside the layers. Finally, we present numerical computations using an adaptive and anisotropic mesh procedure. The chosen examples for drastically different geometries exhibit the variety of situations that can be encountered, and show the efficiency of anisotropic adaptive meshes for this kind of problems.