Symmetric finite volume element approximations of second order linear hyperbolic integro-differential equations

In this paper, based on barycenter dual meshes, we develop one semi-discrete and two full discrete symmetric finite volume element schemes for second order linear hyperbolic integro-differential equations. The optimal order error estimates in L2L2 and H1H1-norms are derived for the semi-discrete scheme. Numerical experiments confirm the performance of the symmetric schemes, and further show that the L2L2-norm convergence rate of the full discrete backward Euler and Crank–Nicolson schemes to be O(h2+τ)O(h2+τ) and O(h2+τ2)O(h2+τ2), respectively.