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.以真解u的单元内部值u0、网格边界值ub及单元内部的梯度▽u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▽u;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.
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.The method contains three variables:u0,ub and▽u,where u0 is the part of the exact solution uin the interior of elements,ub the trace of uon the mesh interface,and!uthe gradient of uin the interior of elements.The method uses discontinuous piecewise polynomials of degrees k,k-1 and k-1(k≥1)to approximate u0,ub and▽u respectively.The time derivative is discretized by the Crack-Nicolson difference scheme.We prove the existence and uniqueness of the solution of the fully discrete scheme of the method.Corresponding error estimates are derived.Numerical experiments are provided to verify the theoretical results.
作者
刘轩宇
罗鲲
王皓
LIU Xuan-Yu;LUO Kun;WANG Hao(School of Mathematics,Sichuan University,Chengdu 610064,China)
出处
《四川大学学报（自然科学版）》
CAS
CSCD
北大核心
2020年第5期830-840,共11页
Journal of Sichuan University(Natural Science Edition)
基金
国家自然科学基金(11771312,11501389)。
