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Volume 14, Issue 3
A Priori and a Posteriori Error Estimates for H(div)-Elliptic Problem with Interior Penalty Method

Yuping Zeng & Jinru Chen

DOI: 10.4208/cicp.040412.071112a

Commun. Comput. Phys., 14 (2013), pp. 753-779.

Published online: 2013-09

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  • Abstract

In this paper, we propose and analyze the interior penalty discontinuous Galerkin method for H(div)-elliptic problem. An optimal a priori error estimate in the energy norm is proved. In addition, a residual-based a posteriori error estimator is obtained. The estimator is proved to be both reliable and efficient in the energy norm. Some numerical testes are presented to demonstrate the effectiveness of our method.


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@Article{CiCP-14-753, author = {Yuping Zeng and Jinru Chen}, title = {A Priori and a Posteriori Error Estimates for H(div)-Elliptic Problem with Interior Penalty Method}, journal = {Communications in Computational Physics}, year = {2013}, volume = {14}, number = {3}, pages = {753--779}, abstract = {

In this paper, we propose and analyze the interior penalty discontinuous Galerkin method for H(div)-elliptic problem. An optimal a priori error estimate in the energy norm is proved. In addition, a residual-based a posteriori error estimator is obtained. The estimator is proved to be both reliable and efficient in the energy norm. Some numerical testes are presented to demonstrate the effectiveness of our method.


}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.040412.071112a}, url = {http://global-sci.org/intro/article_detail/cicp/7180.html} }
TY - JOUR T1 - A Priori and a Posteriori Error Estimates for H(div)-Elliptic Problem with Interior Penalty Method AU - Yuping Zeng & Jinru Chen JO - Communications in Computational Physics VL - 3 SP - 753 EP - 779 PY - 2013 DA - 2013/09 SN - 14 DO - http://doi.org/10.4208/cicp.040412.071112a UR - https://global-sci.org/intro/article_detail/cicp/7180.html KW - AB -

In this paper, we propose and analyze the interior penalty discontinuous Galerkin method for H(div)-elliptic problem. An optimal a priori error estimate in the energy norm is proved. In addition, a residual-based a posteriori error estimator is obtained. The estimator is proved to be both reliable and efficient in the energy norm. Some numerical testes are presented to demonstrate the effectiveness of our method.


Yuping Zeng and Jinru Chen. (2013). A Priori and a Posteriori Error Estimates for H(div)-Elliptic Problem with Interior Penalty Method. Communications in Computational Physics. 14 (3). 753-779. doi:10.4208/cicp.040412.071112a
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