Superconvergence of the discontinuous finite element method for solving first-order hyperbolic problems

作者：Zhang Tie^*; Li Zheng

来源：Journal of Northeastern University, 2012, 33(1): 149-152.

• Discontinuous finite element method
• First-order
• Negative norm error estimate
• Stability and convergence
• Super-convergence

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.

• 出版日期2012
• 单位东北大学