Volume 17, Issue 6
A Conforming Discontinuous Galerkin Finite Element Method: Part III

​Xiu Ye & ​Shangyou Zhang

DOI:

Int. J. Numer. Anal. Mod., 17 (2020), pp. 794-805.

Published online: 2020-10

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  • 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.

  • Keywords

Weak gradient, discontinuous Galerkin, stabilizer/penalty free, finite element methods, second order elliptic problem.

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@Article{IJNAM-17-794, author = {​Xiu Ye , and ​Shangyou Zhang , }, title = {A Conforming Discontinuous Galerkin Finite Element Method: Part III}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2020}, volume = {17}, number = {6}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/18351.html} }
TY - JOUR T1 - A Conforming Discontinuous Galerkin Finite Element Method: Part III AU - ​Xiu Ye , AU - ​Shangyou Zhang , JO - International Journal of Numerical Analysis and Modeling VL - 6 SP - 794 EP - 805 PY - 2020 DA - 2020/10 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/18351.html KW - Weak gradient, discontinuous Galerkin, stabilizer/penalty free, finite element methods, second order elliptic problem. AB -

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.

​Xiu Ye & ​Shangyou Zhang. (2020). A Conforming Discontinuous Galerkin Finite Element Method: Part III. International Journal of Numerical Analysis and Modeling. 17 (6). 794-805. doi:
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