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Volume 12, Issue 4
Achieving Superconvergence by One-Dimensional Discontinuous Finite Elements: The CDG Method

Xiu Ye & Shangyou Zhang

DOI: 10.4208/eajam.121021.200122

East Asian J. Appl. Math., 12 (2022), pp. 781-790.

Published online: 2022-08

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  • Abstract

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.

  • Keywords

Finite element, conforming DG method, stabilizer free, super-convergent.

  • AMS Subject Headings

65N15, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@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 = {

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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.121021.200122}, url = {http://global-sci.org/intro/article_detail/eajam/20884.html} }
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 -

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.

Ye , Xiu and Zhang , Shangyou. (2022). Achieving Superconvergence by One-Dimensional Discontinuous Finite Elements: The CDG Method. East Asian Journal on Applied Mathematics. 12 (4). 781-790. doi:10.4208/eajam.121021.200122
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