An efficient symmetric finite volume element method for second-order variable coefficient parabolic integro-differential equations

This paper is devoted to develop a symmetric finite volume element (FVE) method to solve second-order variable coefficient parabolic integro-differential equations, arising in modeling of nonlocal reactive flows in porous media. Based on barycenter dual mesh, one semi-discrete and two fully discrete backward Euler and Crank-Nicolson symmetric FVE schemes are presented. Then, the optimal order error estimates in L-2-norm are derived for the semi-discrete and two fully discrete schemes. Numerical experiments are performed to examine the convergence rate and verify the effectiveness and usefulness of the new numerical schemes.