TY - JOUR
T1 - Achieving Superconvergence by One-Dimensional Discontinuous Finite Elements: The CDG Method
AU - Ye , Xiu
AU - Zhang , Shangyou
JO - East Asian Journal on Applied Mathematics
VL - 4
SP - 781
EP - 790
PY - 2022
DA - 2022/08
SN - 12
DO - http://doi.org/10.4208/eajam.121021.200122
UR - https://global-sci.org/intro/article_detail/eajam/20884.html
KW - Finite element, conforming DG method, stabilizer free, super-convergent.
AB - <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>