Volume 17, Issue 1
A Conforming Discontinuous Galerkin Finite Element Method

Int. J. Numer. Anal. Mod., 17 (2020), pp. 110-117.

Published online: 2020-02

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• Abstract

A new finite element method with discontinuous approximation is introduced for solving second order elliptic problem. Since this method combines the features of both conforming finite element method and discontinuous Galerkin (DG) method, we call it conforming DG method. While using DG finite element space, this conforming DG method maintains the features of the conforming finite element method such as simple formulation and strong enforcement of boundary condition. Therefore, this finite element method has the flexibility of using discontinuous approximation and simplicity in formulation of the conforming finite element method. Error estimates of optimal order are established for the corresponding discontinuous 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 Galerkin, discontinuous Galerkin, finite element methods, second order elliptic problem.

65N15, 65N30

xxye@ualr.edu (Xiu Ye)

szhang@udel.edu (Shangyou Zhang)

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@Article{IJNAM-17-110, author = {Xiu and Ye and xxye@ualr.edu and 13554 and Department of Mathematics, University of Arkansas at Little Rock, Little Rock, AR 72204, USA. and Xiu Ye and Shangyou and Zhang and szhang@udel.edu and 5543 and Department of Mathematics Science, University of Delaware, Newark 19716, USA and Shangyou Zhang}, title = {A Conforming Discontinuous Galerkin Finite Element Method}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2020}, volume = {17}, number = {1}, pages = {110--117}, abstract = {

A new finite element method with discontinuous approximation is introduced for solving second order elliptic problem. Since this method combines the features of both conforming finite element method and discontinuous Galerkin (DG) method, we call it conforming DG method. While using DG finite element space, this conforming DG method maintains the features of the conforming finite element method such as simple formulation and strong enforcement of boundary condition. Therefore, this finite element method has the flexibility of using discontinuous approximation and simplicity in formulation of the conforming finite element method. Error estimates of optimal order are established for the corresponding discontinuous 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/13643.html} }
TY - JOUR T1 - A Conforming Discontinuous Galerkin Finite Element Method AU - Ye , Xiu AU - Zhang , Shangyou JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 110 EP - 117 PY - 2020 DA - 2020/02 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/13643.html KW - Weak Galerkin, discontinuous Galerkin, finite element methods, second order elliptic problem. AB -

A new finite element method with discontinuous approximation is introduced for solving second order elliptic problem. Since this method combines the features of both conforming finite element method and discontinuous Galerkin (DG) method, we call it conforming DG method. While using DG finite element space, this conforming DG method maintains the features of the conforming finite element method such as simple formulation and strong enforcement of boundary condition. Therefore, this finite element method has the flexibility of using discontinuous approximation and simplicity in formulation of the conforming finite element method. Error estimates of optimal order are established for the corresponding discontinuous 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. International Journal of Numerical Analysis and Modeling. 17 (1). 110-117. doi:
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