Finite element approximation of solutions to a class of nonlinear hyperbolic–parabolic equations Original Research Article

The numerical approximation of Antman and Seidmanʹs (1996) model 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.