A mixed finite element for shell model with free edge boundary conditions Part 2. The numerical scheme

From the mixed variational formulation which was suggested in Part 1, we construct a finite element scheme. Then, a mathematical justification concerning the error estimate is developed. The most important point is to justify two compatibility conditions between the approximation of the kinematics and the stresses. Because of the structure of the shell operator they are not obvious at all and several restrictions on the mesh are necessary. Therefore, the classical result known in fluid mechanics for Stokes equations cannot be applied directly.