  In this article, mixed finite element methods are discussed for a class of
hyperbolic integro-differential equations (HIDEs). Based on a modification of
the nonstandard energy formulation of Baker, both semidiscrete and completely
discrete implicit schemes for an extended mixed method are analyzed and optimal
L^{\infty}(L^2)-error estimates are derived under minimal smoothness
assumptions on the initial data. Further, quasi-optimal estimates are shown to
hold in L^{\infty}(L^{\infty})-norm. Finally, the analysis is extended to the
standard mixed method for HIDEs and optimal error estimates in
L^{\infty}(L^2)-norm are derived again under minimal smoothness on initial
data.
