• Original Articles •

### A PRIORI AND A POSTERIORI ERROR ESTIMATES OF A WEAKLY OVER-PENALIZED INTERIOR PENALTY METHOD FOR NON-SELF-ADJOINT AND INDEFINITE PROBLEMS

Yuping Zeng1, Jinru Chen2, Feng Wang2, Yanxia Meng2

1. 1. School of Mathematics, Jiaying University, Meizhou 514015, China Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China;
2. Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China
• Received:2013-08-27 Revised:2014-03-25 Online:2014-05-15 Published:2014-05-22
• Supported by:

We thank the anonymous referees for their valuable comments and suggestions which lead to an improved presentation of this paper. This work was supported by NSFC under the grant 11371199, 11226334 and 11301275, the Jiangsu Provincial 2011 Program (Collaborative Innovation Center of Climate Change), the Program of Natural Science Research of Jiangsu Higher Education Institutions of China (Grant No. 12KJB110013), Natural Science Foundation of Guangdong Province of China (Grant No. S2012040007993) and Educational Commission of Guangdong Province of China (Grant No. 2012LYM0122).

Yuping Zeng, Jinru Chen, Feng Wang, Yanxia Meng. A PRIORI AND A POSTERIORI ERROR ESTIMATES OF A WEAKLY OVER-PENALIZED INTERIOR PENALTY METHOD FOR NON-SELF-ADJOINT AND INDEFINITE PROBLEMS[J]. Journal of Computational Mathematics, 2014, 32(3): 332-347.

In this paper, we study a weakly over-penalized interior penalty method for non-selfadjoint and indefinite problems. An optimal a priori error estimate in the energy norm is derived. In addition, we introduce a residual-based a posteriori error estimator, which is proved to be both reliable and efficient in the energy norm. Some numerical testes are presented to validate our theoretical analysis.

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