椭圆方程间断有限元方法超收敛性的数值计算  

Numerical calculation of superconvergence with local discontinuous galerkin methods for elliptic equation

作　　者：张作政 ZHANG Zuozheng(College of Computer Engineering and Applied Mathematics,Changsha University,Changsha 410003,China)

机构地区：[1]长沙学院计算机工程与应用数学学院,湖南长沙410003

出　　处：《邵阳学院学报（自然科学版）》2019年第1期36-42,共7页Journal of Shaoyang University：Natural Science Edition

基　　金：湖南省自然科学基金(2018JJ2454);长沙学院科技计划项目(K1705079;K1705021)

摘　　要：针对二维椭圆型方程采用局部间断有限元(LDG)方法求解,理论上证明了椭圆问题LDG解存在唯一性,数值上验证了数值解U的离散误差的主项与每个单元上x与y两个方向上p+1阶右Radau多项式的张量积多项式成比例。对节点处的数值流通量有2p+1阶的超收敛,对单元内部p+1阶右Radau多项式的张量积多项式的右Radau点有p+2阶超收敛。The elliptic equation was solved for local discontinuous galerkin methods(LDG).The existence and uniqueness of the LDG solutions were verified.Numerical calculations showed the leading terms of the local errors for U are spanned by two p+1-order right Radau polynomials in the x and y directions.The 2p+1-order superconvergence of numerical traces at each element were observed.The p+2-order superconvergence at the tensor product of the roots of right Radau polynomials in the x and y directions were showed numerically.

关 键 词：间断有限元 椭圆型方程 超收敛 张量积 

分 类 号：O241.82[理学—计算数学]