Year: 2020
Author: Xiu Ye, Shangyou Zhang
International Journal of Numerical Analysis and Modeling, Vol. 17 (2020), Iss. 6 : pp. 794–805
Abstract
The conforming discontinuous Galerkin (CDG) finite element methods were introduced in [12] on simplicial meshes and in [13] on polytopal meshes. The CDG method gets its name by combining the features of both conforming finite element method and discontinuous Galerkin (DG) finite element method. The goal of this paper is to continue our efforts on simplifying formulations for the finite element method with discontinuous approximation by constructing new spaces for the gradient approximation. Error estimates of optimal order are established for the corresponding CDG finite element approximation in both a discrete $H^1$ norm and the $L^2$ norm. Numerical results are presented to confirm the theory.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2020-IJNAM-18351
International Journal of Numerical Analysis and Modeling, Vol. 17 (2020), Iss. 6 : pp. 794–805
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Weak gradient discontinuous Galerkin stabilizer/penalty free finite element methods second order elliptic problem.