Two stable mixed finite element approximations for the obstacle problem of the Euler-Bernoulli beam

Abstract

We present two finite element approximations of a mixed formulation for the obstacle problem of the Euler-Bernoulli beam problem. The two numerical approximations are based on conforming methods with dual Lagrange multiplier. The first uses a suitable stable pair of finite element spaces. The second proposed scheme employs biorthogonal basis functions. We derive a priori and a posteriori error estimates.  Numerical tests using a primal-dual active set algorithm and the classical Uzawa iteration are given that validate and illustrate our approach.