@Article{EAJAM-12-781,
author = {Ye , Xiu and Zhang , Shangyou},
title = {Achieving Superconvergence by One-Dimensional Discontinuous Finite Elements: The CDG Method},
journal = {East Asian Journal on Applied Mathematics},
year = {2022},
volume = {12},
number = {4},
pages = {781--790},
abstract = {<p style="text-align: justify;">Novelty of this work is the development of a finite element method using
discontinuous $P_k$ element, which has two-order higher convergence rate than the optimal
order. The method is used to solve a one-dimensional second order elliptic problem. A
totally new approach is developed for error analysis. Superconvergence of order two for
the CDG finite element solution is obtained. The $P_k$ solution is lifted to an optimal order $P_{k+2}$ solution elementwise. The numerical results confirm the theory.</p>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.121021.200122},
url = {http://global-sci.org/intro/article_detail/eajam/20884.html}
}