Numerical methods for unilateral problems

摘要

The theory of variational inequalities, besides being elegant and synthetic, also provides a unified general framework for applying the numerical methods for solving many unrelated free boundary value problems. In this paper, we describe numerical experience on the use of variational inequalities and Padé approximants to obtain approximate solutions to a class of unilateral boundary value problems of elasticity, like those describing the equilibrium configuration of an elastic beam stretched over an elastic obstacle. In the case of a known obstacle, these problems can be alternatively formulated as nonlinear boundary value problems without constraints for which the technique of Pade approximants can be successfully employed. The variational inequality formulation is used to discuss the problem of uniqueness and existence of the solution.