Finite Element Approximation of Solutions to a Class of Nonlinear Hyperbolic-Parabolic Equations

The numerical approximation of Antman and Seidman's model [AS] of the longitudinal motion of a viscoelastic rod is investigated. Their constitutive assumptions ensure that infinite compressive stress is needed to produce total compression of the rod. Analyses of the regularity of the solution of the continuous problem, the convergence of a semi-discrete finite element method, and the properties of a space-time finite element scheme are furnished. Results of a sample computation are also provided. 1. Introduction: Consider the following model for the longitudinal motion of a visco-elastic rod: w tt = [n (w s ; w st )] s + f (1) where w = w(s; t) is the position at time t of the point with reference position s so w s is the strain and w st is the strain rate; n is then the contact force and f is the body force. A natural set Work was carried out while French was a visitor at the University of Maryland Baltimore County during 1995-6, at his current position at the University of Cin..