Finite element approximation with quadrature to a time dependent parabolic integro-differential equation with nonsmooth initial data (Q5939772)

The finite element error analysis for parabolic integro-differential equations (IDEs) with non-smooth initial data has been studied extensively, for example by \textit{M. Crouzeix} and \textit{V. Thomée} [Math. Comput. 49, 359-377 (1987; Zbl 0632.65097)] and \textit{V. Thomée} and \textit{N. Y. Zhang} [Math. Comput. 53, No. 187, 121-139 (1989; Zbl 0673.65099)] for exact Galerkin methods, and by \textit{A. K. Pani} and \textit{T. E. Peterson} [SIAM J. Numer. Anal. 33, No. 3, 1084-1105 (1996; Zbl 0858.65141)] in the case where the integrals appearing in the Galerkin formulation are approximated by numerical quadrature.NEWLINENEWLINENEWLINEThe present paper extends these results (including optimal and quasi-optimal \(L^\infty\)-error estimates based on the Ritz-Galerkin projection) to inexact Galerkin methods for time-dependent parabolic IDEs.