Numerical solution of linear quasistatic hereditary viscoelasticity problems

We give a space-time Galerkin finite element discretization of the linear q uasistatic compressible viscoelasticity problem as described by an elliptic partial differential equation with a Volterra ( memory) term. The discreti zation consists of a continuous piecewise linear approximation in space wit h a discontinuous piecewise constant or linear approximation in time. We de rive an a priori maximum energy-error estimate by exploiting Galerkin "orth ogonality" and the data-stability of a related discrete backward problem. I llustrative numerical experiments are also included, as also is a brief des cription of our rst results on a posteriori error estimation. This allows f or adaptive control of the space mesh but not of the time step.