Ye, XiuZhang, Shangyou2022-06-082022-06-082022-04-06Xiu Ye & Shangyou Zhang. (2022). Achieving Superconvergence by One-Dimensional Discontinuous Finite Elements: The CDG Method. East Asian Journal on Applied Mathematics. 12. doi:10.4208/eajam.121021.2001222079-7370https://udspace.udel.edu/handle/19716/30968© Global-Science Press. First published in East Asian Journal on Applied Mathematics in 2022, published by Global Science Press.Novelty of this work is the development of a finite element method using discontinuous Pk 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 Pk solution is lifted to an optimal order Pk+2 solution elementwise. The numerical results confirm the theory.en-USFinite elementconforming DG methodstabilizer freesuper-convergentArticle