NONSMOOTH DATA ERROR-ESTIMATES FOR APPROXIMATIONS OF AN EVOLUTION EQUATION WITH A POSITIVE-TYPE MEMORY TERM

We study the numerical approximation of an integro-differential equati on which is intermediate between the heat and wave equations. The prop osed discretization uses convolution quadrature based on the first- an d second-order backward difference methods in time, and piecewise line ar finite elements in space. Optimal-order error bounds in terms of th e initial data and the inhomogeneity are shown for positive times, wit hout assumptions of spatial regularity of the data.