Numerical Solution of Linear Quasistatic Hereditary Viscoelasticity Problems

We give a space-time Galerkin nite element discretization of the linear quasistatic compressible viscoelasticity problem as described by an elliptic partial diierential equation with a Volterra (memory) term. The discretization consists of a continuous piecewise linear approximation in space with a discontinuous piecewise constant or linear approximation in time. We derive an a priori maximum-energy Galerkin-error estimate by exploiting Galerkin \orthogonality" and the data-stability of a related discrete backward problem. We also describe the form of the numerical algorithm with particular emphasis on the computational advantage of modelling the viscoelastic relaxation functions with a Dirichlet-Prony series. 1. Introduction. For a positive real number T let J := 0; T] denote a time interval, and for n 2 f1; 2; 3g let be a time-independent open bounded domain in