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Acta Mathematicae Applicatae Sinica, English Series 2012, Vol. 28 Issue (1) :117-126    DOI: 10.1007/s10255-012-0127-9
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Some Numerical Quadrature Schemes of a Non-conforming Quadrilateral Finite Element
Xiao-fei GUAN1, Ming-xia LI2, Shao-chun CHEN3
1. Department of Mathematics, Tongji University, Shanghai 200092, China;
2. School of Information Engineering, China University of Geosciences (Beijing), Beijing 100083, China;
3. Department of Mathematics, Zhengzhou University, Zhengzhou 450052, China
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Abstract Numerical quadrature schemes of a non-conforming finite element method for general second order elliptic problems in two dimensional (2-D) and three dimensional (3-D) space are discussed in this paper. We present and analyze some optimal numerical quadrature schemes. One of the schemes contains only three sampling points, which greatly improves the efficiency of numerical computations. The optimal error estimates are derived by using some traditional approaches and techniques. Lastly, some numerical results are provided to verify our theoretical analysis.  
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Keywordsnumerical integration   non-conforming quadrilateral finite element   optimal error estimate     
Abstract: Numerical quadrature schemes of a non-conforming finite element method for general second order elliptic problems in two dimensional (2-D) and three dimensional (3-D) space are discussed in this paper. We present and analyze some optimal numerical quadrature schemes. One of the schemes contains only three sampling points, which greatly improves the efficiency of numerical computations. The optimal error estimates are derived by using some traditional approaches and techniques. Lastly, some numerical results are provided to verify our theoretical analysis.  
Keywordsnumerical integration,   non-conforming quadrilateral finite element,   optimal error estimate     
Received: 2009-07-01;
Fund:

Supported by the National Natural Science Foundation of China (No. 50838004, 50908167). The second author’s work is supported by the Fundamental Research Funds for the Central Universities of China (No. 2011YYL078) and the National Natural Science Foundation of China (No. 11101386).

Cite this article:   
.Some Numerical Quadrature Schemes of a Non-conforming Quadrilateral Finite Element[J]  Acta Mathematicae Applicatae Sinica, English Serie, 2012,V28(1): 117-126
URL:  
http://www.applmath.com.cn/jweb_yysxxb_en/EN/10.1007/s10255-012-0127-9      或     http://www.applmath.com.cn/jweb_yysxxb_en/EN/Y2012/V28/I1/117
 
[1] Babuška, I. Error-bounds for finite element method. Numer. Math., 16: 322-333 (1971)
[2] Ciarlet, P.G. The finite element method for elliptic problems. North-Holland, Amsterdam, 1978
[3] Courant, R. Variational methods for the solution of problems of equilibrium and vibrations. Bull. Amer. Math. Soc., 49: 1-23 (1943)
[4] Douglas, Jr. J., Santos, J.E., Sheen, D., Ye, X. Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems. RAIRO Model Math. Anal. Numer., 33: 747-770 (1999)
[5] Han, H.D. Nonconforming elements in the mixed finite element methods. J. Comput. Math, 2: 12-23 (1984)
[6] He, W.M., Cui, J.Z. A finite element method for elliptic problems with rapidly oscillating coefficients. BIT Numer. Math., 47: 77-102 (2007)
[7] Irons, B.M. Quadrature rules for brick based finite elements. Int. J. Num. Meth. Eng., 3: 293-294 (1971)
[8] Irons, B.M., Razzaque A. Experience with the patch test for convergence of finite element. In: The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, Academic Press, New York, 1972, 557-587
[9] Ming, P.B. Nonconforming elements vs locking problems. Ph. D dissertation, Chinese Academy of Sciences, 1999
[10] Ming, P.B., Shi, Z.-C. Quadrilateral mesh revisited. Comput. Methods Appl. Mech. Engrg., 191: 5671-5682 (2002)
[11] Ming, P.B., Shi, Z.-C. Mathmatical analysis for quadrilateral rotated Q1 elements III: the effect of numerical integration. J. Comput. Math, 21: 287-294 (2003)
[12] Ming, P.B., Shi, Z.-C., Xu, X.Y. A new superconvergence property of non-conforming rotated Q1 element in 3D. Comput. Methods Appl. Mech. Engrg., 197: 95-102 (2007)
[13] Rannacher, R., Turek, S. A simple non-conforming quadrilateral Stokes element. Numer. Meth. PDEs, 8: 97-111 (1992)
[14] Shi, Z.-C. A convergence condition for the quadrilateral Wilson element. Numer. Math., 44: 349-361 (1984)
[15] Stummel, F. The generalized patch test. SIAM J. Numer. Anal., 16: 449-471 (1979)
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