Paper Titles

A Two-Stage Hybrid Algorithm for Flexible Job-Shop Scheduling
p.476

Some Research about Technology of Disaster Tolerance for Data Center
p.482

Design and Development of a New Automated and High Speed Cap Sealing System
p.489

3D Numerical Combustion Simulation of Designed Low Heating Value Fuel Combustor for Further Detail Modulation
p.494

Convergence Analysis for Cubic Serendipity Finite Elements with Thirty-Two Degrees of Freedom
p.501

Model Reference Adaptive Control on a Hydraulic Servo System
p.505

Simulation Studies on Model Reference Adaptive Controller for Permanent Magnet Synchronous Motor Drive
p.509

Speed Regulation of a Permanent Magnet Synchronous Motor via Model Reference Adaptive Control
p.513

A Prediction Based Data Aggregation Scheme in Wireless Sensor Networks
p.517

HomeAdvanced Materials ResearchAdvanced Materials Research Vols. 268-270Convergence Analysis for Cubic Serendipity Finite...

Convergence Analysis for Cubic Serendipity Finite Elements with Thirty-Two Degrees of Freedom

Article Preview

Abstract:

In this paper, we consider the Poisson problem with homogeneous Dirichlet boundary conditions on the bounded open domain and analyze convergence phenomena that appear by using cubic serendipity block elements with thirty-two degrees of freedom. By means of the standard Legendre polynomial technique, we derive an error estimate, which is not superconvergent and shows this serendipity element has not pointwise supercloseness properties.

You might also be interested in these eBooks

Computational Materials Science

Info:

Periodical:

Advanced Materials Research (Volumes 268-270)

Pages:

501-504

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.268-270.501

Citation:

Cite this paper

Online since:

July 2011

Authors:

Jing Hong Liu, Xiao Cheng Huo

Keywords:

Cubic Serendipity Elements, Interpolation Operator of Projection Type, Supercloseness

Export:

RIS, BibTeX

Price:

Permissions CCC:

Request Permissions

Permissions PLS:

Request Permissions

Сopyright:

© 2011 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

[1] J. H. Brandts and M. Krizek: History and future of superconvergence in three dimensional ﬁnite element methods, Proceedings of the Conference on Finite Element Methods: Three-dimensional Problems, GAKUTO International Series Mathematics Science Application, Gakkotosho, Tokyo, 15 (2001).

[2] J. H. Brandts and M. Krizek: Gradient superconvergence on uniform simplicial partitions of polytopes, IMA J. Numer. Anal. 23 (2003), 489–505.

DOI: 10.1093/imanum/23.3.489

[3] J. H. Brandts and M. Krizek: Superconvergence of tetrahedral quadratic ﬁnite elements, J. Comput. Math. 23 (2005), 27–36.

[4] C. M. Chen: Optimal points of stresses for the linear tetrahedral element (in Chinese), Nat. Sci. J. Xiangtan Univ. 3 (1980), 16–24.

[5] C. M. Chen: Construction theory of superconvergence of ﬁnite elements (in Chinese), Hunan Science and Technology Press, Changsha, China, (2001).

[6] L. Chen: Superconvergence of tetrahedral linear ﬁnite elements, Internat. J. Numer. Anal. Model. 3 (2006), 273–282.

[7] G. Goodsell: Gradient superconvergence for piecewise linear tetrahedral ﬁnite el- ements, Technical Report RAL-90-031, Science and Engineering Research Council, Rutherford Appleton Laboratory, (1990).

[8] G. Goodsell: Pointwise superconvergence of the gradient for the linear tetrahedral element, Numer. Methods Partial Differential Equations 10 (1994), 651–666.

DOI: 10.1002/num.1690100511

[9] V. Kantchev and R. D. Lazarov: Superconvergence of the gradient of linear ﬁnite elements for 3D Poisson equation, B. Sendov, editor, Proceedings of the Conference on Optimal Algorithms, Bulgarian Academy of Sciences, Soﬁa, 1986, p.172–182.

[10] Q. Lin and N. N. Yan: Construction and analysis of high efficient ﬁnite elements (in Chinese), Hebei University Press, Baoding, China, (1996).

[11] R. C. Lin and Z. M. Zhang: Natural superconvergent points in 3D ﬁnite elements, SIAM J. Numer. Anal. 46 (2008), 1281–1297.

[12] J. H. Liu and Q. D. Zhu: Uniform superapproximation of the derivative of tetra- hedral quadratic ﬁnite element approximation, J. Comput. Math. 23 (2005), 75–82.

[13] J. H. Liu and Q. D. Zhu: Maximum-norm superapproximation of the gradient for the trilinear block ﬁnite element, Numer. Methods Partial Differential Equations 23 (2007), 1501–1508.

DOI: 10.1002/num.20237

[14] J. H. Liu and Q. D. Zhu: Pointwise supercloseness of tensor-product block ﬁnite elements, Numer. Methods Partial Differential Equations 25 (2009), 990–1008.

DOI: 10.1002/num.20384

[15] J. H. Liu and Q. D. Zhu: Pointwise supercloseness of pentahedral ﬁnite elements, Numer. Methods Partial Differential Equations 26 (2010), 1572–1580.

DOI: 10.1002/num.20510

[16] A. Pehlivanov: Superconvergence of the gradient for quadratic 3D simplex ﬁnite elements, Proceedings of the Conference on Numerical Methods and Application, Bulgarian Academy of Sciences, Soﬁa, 1989, p.362–366.

[17] A. H. Schatz, I. H. Sloan and L. B. Wahlbin, Superconvergence in ﬁnite element methods and meshes that are locally symmetric with respect to a point, SIAM J. Numer. Anal. 33 (1996), 505–521.

DOI: 10.1137/0733027

[18] Z. M. Zhang and R. C. Lin: Locating natural superconvergent points of ﬁnite element methods in 3D, Internat. J. Numer. Anal. Model. 2 (2005), 19–30.

[19] M. Zlamal: Superconvergence and reduced integration in the ﬁnite element method, Math. Comp. 32 (1978), 663–685.

DOI: 10.1090/s0025-5718-1978-0495027-4

[20] J. H. Liu, D. C. Yin and Q. D. Zhu: A note on superconvergence of recovered gradients of tensor-product linear pentahedral ﬁnite element approximations. Proceedings of the 3rd International Conference on Computational Intelligence and Industrial Application 3 (2010).

DOI: 10.1109/icicis.2011.65

[21] J. H. Liu, X. C. Huo and Q. D. Zhu: Pointwise supercloseness of quadratic serendipity block finite elements for a variable coefficient elliptic equation, Numer. Methods Partial Differential Equations. (published online).

DOI: 10.1002/num.20580

[22] J. H. Liu and Q. D. Zhu: The estimate for the W1, 1-seminorm of discrete derivative Green's function in three dimensions (in Chinese), J. Hunan Univ. Arts Sci. 16 (2004), 1-3.