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


A Priori and a Posteriori Error Estimates for H(div)-Elliptic Problem with Interior Penalty Method

Yuping Zeng 1, Jinru Chen 1*

1 Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China.

Received 4 April 2012; Accepted (in revised version) 7 November 2012
Available online 28 February 2013
doi:10.4208/cicp.040412.071112a

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.

AMS subject classifications: 65N15, 65N30

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Key words: Discontinuous Galerkin method, H(div)-elliptic problem, a priori error estimate, a posteriori error estimate.

*Corresponding author.
Email: yuping_zeng@163.com (Y. Zeng), jrchen@njnu.edu.cn (J. Chen)
 

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