间断有限元求解两点边值椭圆问题的超收敛性数值研究

Numerical Calculation of Superconvergence with Discontinuous Galerkin Methods for Two Boundary Values Problems

基于局部间断有限元(LDG)方法求解两点边值问题.数值上验证了对于md-LDG方法,P+1阶的右Radau点与左Radau点分别是数值解U和导数Q的P+2阶超收敛点.对于一致且守恒的间断有限元法,在数值解导数Q处,P阶Gauss点是P+1阶的超收敛.

In this paper, a numerical study of the superconvergence points of a class of discontinuous Galerkin methods for an one-dimensional elliptic equation is presented. For md-LDG method, the P+1 degree right Radau points and left Radau points are the P + 2 degree superconvergence points for U and Q, respectively. For other well-defined consistent and conservative DG methods, only the P degree Gauss points are the P + 1 order superconvergence points for Q.