The Reduced Basis Method for an Elastic Buckling Problem

In this work, we apply the Reduced Basis (RB) Method to the field of nonlinear elasticity. In this first stage of research, we analyze a buckling problem for a compressed 2D column: Here, the trivial linear solution is computed for an arbitrary load; the critical load, marking the transition to nonlinearity, is then identified through an eigenvalue problem. The linear problem satisfies the Lax‐Milgram conditions, allowing the implementation of both a Successive Constraint Method for an inexpensive lower bound of the coercivity constant and of a rigorous and efficient a posteriori error estimator for the RB approximation. Even though only a non‐rigorous estimator is available for the buckling problem, the actual RB approximation of the output is more than satisfactory, and the gain in computational efficiency significant. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)