Backward Euler type methods for parabolic integro-differential equations in Banach space

Time discretization by backward Euler type methods for a parabolic equation with memory is studied. Stability and error estimates are proved under conditions that permit quadrature rules for approximation of the memory term that have reduced storage requirements. The analysis takes place in a Banach space framework, and the results are used to derive error estimates in the L-2 and maximum norms for piecewise linear finite element discretization in two space dimensions. (C) Elsevier, Paris.