Numerical analysis of elastica with obstacle and adhesion effects

We consider numerical analysis of a variational problem arising from materials science. The target functional is a type of Euler's elastica energy that is influenced by obstacles and adhesion. Owing to its strong nonlinearity and discontinuity, the Euler-Lagrange equation is very complicated, and numerical computation of its critical points is difficult. In this paper, we discretize and regularize the target energy as a functional defined on a space of polygonal curves. Moreover, we discuss convergence analysis for discrete minimizers in the framework of Gamma-convergence. We first show that the discrete energy functional Gamma-converges to the original one under the constraint that W-1,W-infinity-norm is bounded. Then, we establish the compactness property for the sequence of discrete minimizers under the same constraint. These two results allow us to extract a convergent subsequence from the discrete minimizers. We also present some numerical examples in the last part of the paper. Existence of singular localminimizers is suggested by numerical experiments.