解一阶双曲问题间断有限元方法的超收敛性质

Superconvergence of the Discontinuous Finite Element Method for Solving First-Order Hyperbolic Problems

研究求解一阶双曲问题的间断有限元方法并分析方法的稳定性和收敛性.对于k次间断有限元,利用对偶论证技术建立了在求解区域和某些子区域上的负模误差估计.利用负模误差估计进一步证明了间断有限元解在这些区域和它们的流出边界上均值逼近具有O(h2k+1/2)阶超收敛性质.数值实例验证了理论分析结果.

The discontinuous finite element method for solving the first-order hyperbolic problems was studied and the stability and convergence of this method were analyzed. For the k-order discontinuous finite elements, the negative norm error estimates are established on the solution domain and some suitably chosen subdomains by using the dual argument technique. Further, based on the negative norm error estimates, the O（h2k ＋ 1/2）-order superconvergence is shown for the error on average on these domains and their outflow faces. These theoretical results are verified by numerical experiments.