Numerical solution to a one-dimensional thermoplastic problem with unilateral constraint

Abstract

In this article, we present a numerical simulation of one-dimensional problem of quasi-static contact with an elastic obstacle. A finite difference scheme is derived by the method of reduction of order on uniform meshes. The stability and convergence are proved. The convergence order is of O(τ2 + h2), where τ and h are the time step size and the space step size, respectively. Some numerical examples demonstrate the theoretical results. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005