Achieving Superconvergence by One-Dimensional Discontinuous Finite Elements: The CDG Method
Date
2022-04-06
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
East Asian Journal on Applied Mathematics
Abstract
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.
Description
© Global-Science Press. First published in East Asian Journal on Applied Mathematics in 2022, published by Global Science Press.
Keywords
Finite element, conforming DG method, stabilizer free, super-convergent
Citation
Xiu 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.121021.200122