On the finite volume element method for self-adjoint parabolic integrodifferential equations (Q2337043)

Summary: Finite volume element schemes for non-self-adjoint parabolic integrodifferential equations are derived and stated. For the spatially discrete scheme, optimal-order error estimates in \(L^2\), \(H^1\), and \(L^p\), \(W^{1, p}\) norms for \(2 \leq p <\infty\), are obtained. In this paper, we also study the lumped mass modification. Based on the Crank-Nicolson method, a time discretization scheme is discussed and related error estimates are derived.