A mixed discontinuous finite element method for folded Naghdi’s shell in Cartesian coordinates

Source abstract

In this work a mixed method and its DG formulation are proposed to solve Naghdi’s equations for a thin linearly elastic shell. The unknowns of the problem are the displacement of the points of the middle surface, the rotation field of the normal vector to the middle surface of the shell and a Lagrange multiplier which is introduced in order to enforce the tangency requirement on the rotation. In addition to existence and uniqueness results of solutions of the continuous and the discrete problems we derive an a priori error estimate. We further propose an a posteriori estimator that yields an upper bound and a lower bound of the error. Numerical tests that validate and illustrate our approach are given.