Numerical Solution of Linear Quasistatic Hereditary Viscoelasticity Problems

Abstract

We give a space-time Galerkin finite element discretization of the linear quasistatic compressible viscoelasticity problem as described by an elliptic partial differential 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-error estimate by exploiting Galerkin "orthogonality" and the data-stability of a related discrete backward problem. Illustrative numerical experiments are also included, as also is a brief description of our first results on a posteriori error estimation. This allows for adaptive control of the space mesh but not of the time step.