抛物型积分微分方程的全离散界面修正直接间断有限元法
The DDGIC Method for Parabolic Integro-differential Equations
谌超凡 1郑云英 1卜斌1
作者信息
摘要
针对线性抛物型积分微分方程,首先利用带界面修正的直接间断有限元(DDGIC)法对空间离散,分析半离散格式的稳定性;然后在时间方向应用Crank-Nicolson法,建立全离散的Crank-Nicolson/DDGIC格式,对全离散格式的收敛性进行了详细讨论;最后给出数值算例验证方法的有效性和理论结果.
Abstract
In this paper,DDGIC(Direct discontinuous Galerkin finite element method with interface correction)is applied to numerical solving the linear parabolic integro-differential equation,and the stability of semi-discrete scheme is discussed.Then with Crank-Nicolson discretion adopted in time direction,the fully discrete scheme is got,and the convergence is analyzed in detail.The numerical examples are given to verify the validity and the theoretical results.
关键词
抛物型积分微分方程/界面修正的直接间断有限元法/Crank-Ni-colson/法Key words
Linear parabolic integro-differential equations/Direct discontinuous Galerkin finite element method with interface correction/Crank-Nicolson $ method引用本文复制引用
基金项目
安徽省自然科学基金(2008085MA11)
安徽省高校自然科学基金(KJ2018A0385)
出版年
2024
NETL
NSTL
万方数据