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Achieving Superconvergence by One-Dimensional Discontinuous Finite Elements: The CDG Method

Achieving Superconvergence by One-Dimensional Discontinuous Finite Elements: The CDG Method
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Year:    2022

Author:    Xiu Ye, Shangyou Zhang

East Asian Journal on Applied Mathematics, Vol. 12 (2022), Iss. 4 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.121021.200122

East Asian Journal on Applied Mathematics, Vol. 12 (2022), Iss. 4 : pp. 781–790

Published online:    2022-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    10

Keywords:    Finite element conforming DG method stabilizer free super-convergent.

Author Details

Xiu Ye

Shangyou Zhang

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