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.

中文翻译：

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二阶变系数抛物线积分微分方程的有效对称有限体积元方法

本文致力于发展一种对称有限体积单元法（FVE），用于求解在多孔介质中非局部反应流建模中产生的二阶变系数抛物线积分微分方程。基于重心双网格，提出了一种半离散和两种完全离散的后向欧拉和曲柄-尼科尔森对称FVE方案。然后，针对半离散和两个完全离散方案导出\（L ^ {2} \）- norm中的最佳顺序误差估计。进行数值实验以检验收敛速度并验证新数值方案的有效性和实用性。