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 L 2 and H 1 -norms are derived for the semi-discrete scheme. Numerical experiments confirm the performance of the symmetric schemes, and further show that the L 2 -norm convergence rate of the full discrete backward Euler and Crank-Nicolson schemes to be O ( h 2 + ? ) and O ( h 2 + ? 2 ) , respectively.

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