一维Lagrange四次元有限体积法的超收敛性

Superconvergence of One Dimension Lagrange Fourth-Order Finite Volume Element Method

通过取等距节点四次Lagrange插值的导数超收敛点作为对偶单元的节点,取Lagrange型四次有限元空间为试探函数空间,取相应于对偶剖分的分片常数函数空间为检验函数空间的方法,得到了求解两点边值问题的四次元有限体积法,证明了该方法具有最优的H1模和L2模误差估计,并讨论了对偶单元节点的导数超收敛估计.数值实验验证了理论分析结果.

We chose fourth order Lagrange interpolated function associated with the nodes as trial function,piecewise constant function as test function,and derivative superconvergent points as dual partition nodes so that a new kind of Lagrange fourth order finite volume element method was obtained for solving two-point boundary value problems.It was proved that the method has optimal H1 and L2 error estimates.The superconvergence of numerical derivatives was discussed.Finally,the numerical experiments show the results of theoretical analysis.