A penalty method for a linear Koiter shell model

Abstract

In this paper a penalized method and its approximation by finite element method are proposed to solve Koiter’s equations for a thin linearly elastic shell. In addition to existence and uniqueness results of solutions of the continuous and the discrete problems we derive some a priori error estimates. We are especially interested in the behavior of the solution when the penalty parameter goes to zero. We propose here a new formulation that leads to a quasi optimal and uniform error estimate with respect to the penalized parameter. In other words, we are able to show that this method converges uniformly with respect to the penalized parameter and to the mesh size. Numerical tests that validate and illustrate our approach are given.