Negative norm error control for second-kind convolution Volterra equations

Summary. We consider a piecewise constant finite element approximation to the convolution Volterra equation problem of the second kind: find such that in a time interval . An a posteriori estimate of the error measured in the norm is developed and used to provide a time step selection criterion for an adaptive solution algorithm. Numerical examples are given for problems in which is of a form typical in viscoelasticity theory. Received March 5, 1998 / Revised version received November 30, 1998 / Published online December 6, 1999