Finite element method for a class of parabolic integro-differential equations with interfaces

Abstract

In this paper, convergence of finite element method for a class of parabolic integro-differential equations with discontinuous coefficients are analyzed. Optimal L2(L2) and L2 (H1) norms are shown to hold when the finite element space consists of piecewise linear functions on a mesh that do not require to fit exactly to the interface. Both continuous time and discrete time Galerkin methods are discussed for arbitrary shape but smooth interfaces.