Journal of Computational Mathematics
 Home    About Journal    Information for Authors    Editorial Board    Subscribe    Editorial Office
Journal of Computational Mathematics 2012, Vol. 30 Issue (4) :337-353    DOI: 10.4208/jcm.1108-m3677
Original Articles Current Issue | Next Issue | Archive | Adv Search << | Next Articles >>
EXPLICIT ERROR ESTIMATES FOR COURANT, CROUZEIX-RAVIART AND RAVIART-THOMAS FINITE ELEMENT METHODS
Carsten Carstensen1,2, Joscha Gedicke1, Donsub Rim3
1. Institut fur Mathematik, Humboldt-Universitat zu Berlin, Unter den Linden 6, 10099 Berlin, Germany;
2. Department of Computational Science and Engineering, Yonsei University, 120-749 Seoul, Korea;
3. Yonsei School of Business and Department of Computational Science and Engineering, Yonsei University, 120-749 Seoul, Korea

Download: PDF (430KB)   HTML (1KB)   Export: BibTeX or EndNote (RIS)      Supporting Info
Abstract The elementary analysis of this paper presents explicit expressions of the constants in the a priori error estimates for the lowest-order Courant, Crouzeix-Raviart nonconforming and Raviart-Thomas mixed nite element methods in the Poisson model problem. The three constants and their dependences on some maximal angle in the triangulation are indeed all comparable and allow accurate a priori error control.
Service
Email this article
Add to my bookshelf
Add to citation manager
Email Alert
RSS
Articles by authors
Carsten Carstensen
Joscha Gedicke
Donsub Rim
MSC2000:

65N15, 65N12, 65N30

;
KeywordsError estimates   Conforming   Nonconforming   Mixed   Finite element method     
Received: 2011-02-10; published: 2012-07-06
Cite this article:   
Carsten Carstensen, Joscha Gedicke, Donsub Rim .EXPLICIT ERROR ESTIMATES FOR COURANT, CROUZEIX-RAVIART AND RAVIART-THOMAS FINITE ELEMENT METHODS[J]  Journal of Computational Mathematics, 2012,V30(4): 337-353
URL:  
http://www.jcm.ac.cn/EN/10.4208/jcm.1108-m3677      OR     http://www.jcm.ac.cn/EN/Y2012/V30/I4/337
 
[1] D. Braess, Finite elements, Cambridge University Press, Cambridge, second edition, 2001, Theory,fast solvers, and applications in solid mechanics, Translated from the 1992 German edition byLarry L. Schumaker.
[2] P.G. Ciarlet, The nite element method for elliptic problems, volume 4 of Studies in Mathematicsand its Applications, North-Holland Publishing Co., Amsterdam, 1978.
[3] F. Kikuchi and X. Liu, Estimation of interpolation error constants for the P0 and P1 triangular nite elements, Comput. Methods Appl. Mech. Engrg., 196:37-40 (2007), 3750{3758.
[4] I. Babu ska and A.K. Aziz, On the angle condition in the nite element method, SIAM J. Numer.Anal., 13:2 (1976), 214{226.
[5] G. Acosta and R.G. Dur an, The maximum angle condition for mixed and nonconforming elements:application to the Stokes equations, SIAM J. Numer. Anal., 37:1 (1999), 18{36.
[6] S.C. Brenner and L.R. Scott, The mathematical theory of nite element methods, volume 15 ofTexts in Applied Mathematics, Springer, New York, third edition, 2008.
[7] S. Mao and Z. Shi, Explicit error estimates for mixed and nonconforming nite elements, J.Comput. Math., 27:4 (2009), 425{440.
[8] L.D. Marini, An inexpensive method for the evaluation of the solution of the lowest order Raviart-Thomas mixed method, SIAM J. Numer. Anal., 22:3 (1985), 493{496.
[9] D.N. Arnold and F. Brezzi, Mixed and nonconforming nite element methods: implementation,postprocessing and error estimates, RAIRO Mod el. Math. Anal. Num er., 19:1 (1985), 7{32.
[10] L.E. Payne and H.F. Weinberger, An optimal Poincar e inequality for convex domains, Arch.Rational Mech. Anal., 5 (1960), 286{292.
[11] R.S. Laugesen and B.A. Siudeja, Minimizing Neumann fundamental tones of triangles: an optimalPoincar e inequality, J. Di erential Equations, 249:1 (2010), 118{135.
No related similar found!
Copyright 2010 by Journal of Computational Mathematics