抛物型积分微分方程的新型全离散弱 Galerkin 有限元法

A new fully discrete weak Galerkin finite element method for parabolic integro-differential equations

摘要:

本文研究基于任意多边形/多面体网格求解二维和三维抛物型积分微分方程的一类全离散弱Galerkin有限元法.本文以真解u的单元内部值u0、网格边界值ub以及单元内部的梯度为变量，弱Galerkin法在空间上采用间断的分片k次，k-1次，k-1(k≥1)次多项式来分别逼近u0，ub和内部梯度,并采用Crack-Nicolson差分格式对时间导数项进行离散.本文证明了全离散格式解的存在唯一性，导出了相应的误差估计.数值实验验证了理论结果.

Abstract:

In this paper, we study a fully discrete weak Galerkin finite element method for solving parabolic integro-differential equations baesd on polygons/polyhedrons mesh of any shape. We prove the existence and uniqueness of the solutions of the fully discrete schemes of the method. Corresponding error estimates are derived. Numerical experiments are provided to verify the theoretical results.