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

摘要

In this paper, convergence of finite element method for a class of parabolic integro-differential equations with discontinuous coefficients are analyzed. Optimal L 2(L 2) and L 2 (H 1) 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.