A posteriori analysis of penalized and mixed formulations of Koiter’s shell model

We are interested in finite element approximations of a Koiter model for linearly elastic shells with little regularity. To perform conforming method, we present a penalized and a mixed formulations of the model allowing to approximate and to enforce weakly mechanical constraints, respectively. We establish existence and uniqueness of the solution to the both formulations. Moreover, a posteriori analysis is led yielding an upper bound and a lower bound of the error. Finally, numerical results are presented to illustrate the efficiency of the a posteriori estimators. We therefore, propose a mesh adaptivity strategy relying on these indicators.