A POSTERIORI ERROR ESTIMATION OF THE NEW MIXED ELEMENT SCHEMES FOR SECOND ORDER ELLIPTIC PROBLEM ON ANISOTROPIC MESHES

doi:10.1016/S0252-9602(14)60100-4

数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (5): 1510-1518.doi: 10.1016/S0252-9602(14)60100-4

A POSTERIORI ERROR ESTIMATION OF THE NEW MIXED ELEMENT SCHEMES FOR SECOND ORDER ELLIPTIC PROBLEM ON ANISOTROPIC MESHES

王培珍^1,2|陈绍春¹

1. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450052, China；
2. School of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou 450011, China

收稿日期:2013-03-13 修回日期:2014-04-23 出版日期:2014-09-20 发布日期:2014-09-20
基金资助:
This work is supported by NSFC (11371331).

A POSTERIORI ERROR ESTIMATION OF THE NEW MIXED ELEMENT SCHEMES FOR SECOND ORDER ELLIPTIC PROBLEM ON ANISOTROPIC MESHES

WANG Pei-Zhen^1,2, CHEN Shao-Chun¹

1. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450052, China；
2. School of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou 450011, China

Received:2013-03-13 Revised:2014-04-23 Online:2014-09-20 Published:2014-09-20
Supported by:
This work is supported by NSFC (11371331).

摘要/Abstract

摘要：

This paper presents a posteriori residual error estimator for the new mixed el-ement scheme for second order elliptic problem on anisotropic meshes. The reliability and efficiency of our estimator are established without any regularity assumption on the mesh. Key words error estimator; anisotropic meshes; new mixed element schemes

关键词: error estimator, anisotropic meshes, new mixed element schemes

Abstract:

Key words: error estimator, anisotropic meshes, new mixed element schemes

中图分类号:

65N30

王培珍, 陈绍春. A POSTERIORI ERROR ESTIMATION OF THE NEW MIXED ELEMENT SCHEMES FOR SECOND ORDER ELLIPTIC PROBLEM ON ANISOTROPIC MESHES[J]. 数学物理学报(英文版), 2014, 34(5): 1510-1518.

WANG Pei-Zhen, CHEN Shao-Chun. A POSTERIORI ERROR ESTIMATION OF THE NEW MIXED ELEMENT SCHEMES FOR SECOND ORDER ELLIPTIC PROBLEM ON ANISOTROPIC MESHES[J]. Acta mathematica scientia,Series B, 2014, 34(5): 1510-1518.

参考文献

[1] Alonso A. Error estimators for mixed methods. Numer Math, 1996, 74: 385–395

[2] Braess D, Verfurth R. A posteriori error estimators for the Raviart-Thomas element. SIAM J Numer Anal, 1996, 33: 2431–2444

[3] Carstensen C. A posteriori error estimate for the mixed finite element method. Math Comp, 1997, 66: 465–476

[4] Chen S C, Chen H R. New mixed element schemes for second order elliptic problem (in Chinese). Mathematica
Numerica Sinica, 2010, 32(2): 213–218

[5] Ciarlet P G. The Finite Method for Elliptic Problem. Amsterdam: North-Holland, 1978

[6] Clement P. Approximation by finite element functionsusing local regularization. RAIRO Anal Numer, 1975, R-2: 77–84

[7] Creuse E, Kunert G, Nicaise S. A posteriori error estimation for the stokes problem: Anisotropic and isotropic discretizations. Math Models Methods Appl Sci, 2004, 14: 1297–1341

[8] Kunert G. A Posteriori Error Estimation for Anisotropic Tetrahedral and Triangular Finite Element Meshes. Berlin: Logos Verlag, 1999

[9] Luo Z D. Mixed Finite Element Methods and Applications (in Chinese). Beijing: Chinese Science Press, 2006

[10] Luo Z D. Analysis of some mixed finite elements methods for second order elliptic equations (in Chinese). Math Appl, 1992, 5(4): 26–31

[11] Luo Z D. Mixed finite element estimates for second order elliptic problems (in Chinese). Acta Math Appl Sin, 1993, 16(4): 473–476

[12] Nicaise S, Creuse E. Isotropic and anisotropic a posteriori error estimation of the mixed finite element method for second order operators in divergence form. Elect Tran Numer Anal, 2006, 23: 38–62

[13] Raviart P A, Thomas J M. A Mixed Finite Element Method for Second Order Elliptic Problems. Lecture Notes in Math 606. Berlin: Springer-Verlag, 1977: 292–315

[14] Siebert K G. An a posteriori error estimator for anisotropic refinement. Numer Math, 1996, 73(3): 373–398

[15] Verf¨urth R. A review of a posteriori error estimation and adaptive mesh-refinement techniques. Wiley-Teubner, Chichester; Stuttgart, 1996

[16] Zhao J K, Chen S C. Explicit error estimate for the nonconforming Wilson´s element. Acta Math Sci, 2013, 33B(3): 839–846

A POSTERIORI ERROR ESTIMATION OF THE NEW MIXED ELEMENT SCHEMES FOR SECOND ORDER ELLIPTIC PROBLEM ON ANISOTROPIC MESHES

A POSTERIORI ERROR ESTIMATION OF THE NEW MIXED ELEMENT SCHEMES FOR SECOND ORDER ELLIPTIC PROBLEM ON ANISOTROPIC MESHES

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