Browse > Article
http://dx.doi.org/10.12941/jksiam.2012.16.1.001

A POSTERIORI ERROR ESTIMATOR FOR LINEAR ELASTICITY BASED ON NONSYMMETRIC STRESS TENSOR APPROXIMATION  

Kim, Kwang-Yeon (DEPARTMENT OF MATHEMATICS, KANGWON NATIONAL UNIVERSITY)
Publication Information
Journal of the Korean Society for Industrial and Applied Mathematics / v.16, no.1, 2012 , pp. 1-13 More about this Journal
Abstract
In this paper we present an a posteriori error estimator for the stabilized P1 nonconforming finite element method of the linear elasticity problem based on a nonsymmetric H(div)-conforming approximation of the stress tensor in the first-order Raviart-Thomas space. By combining the equilibrated residual method and the hypercircle method, it is shown that the error estimator gives a fully computable upper bound on the actual error. Numerical results are provided to confirm the theory and illustrate the effectiveness of our error estimator.
Keywords
a posteriori error estimator; linear elasticity; P1 nonconforming finite element method;
Citations & Related Records
연도 인용수 순위
  • Reference
1 R. Verfurth, A review of a posteriori error estimation techniques for elasticity problems, Comput. Methods Appl. Mech. Engrg., 176 (1999), 419-440.   DOI   ScienceOn
2 S. Nicaise, K. Witowski and B.I. Wohlmuth, An a posteriori error estimator for the Lame equation based on equilibrated fluxes, IMA J. Numer. Anal., 28 (2008), 331-353.
3 M. Ainsworth and R. Rankin, Guaranteed computable error bounds for conforming and nonconforming finite element analyses in planar elasticity, Internat. J. Numer. Methods Engrg., 82 (2010), 1114-1157.   DOI   ScienceOn
4 H.-C. Lee and K.-Y. Kim, A posteriori error estimators for stabilized P1 nonconforming approximation of the Stokes problem, Comput. Methods Appl. Mech. Engrg., 199 (2010), 2903-2912.   DOI   ScienceOn
5 P. Hansbo and M.G. Larson, Discontinuous Galerkin and the Crouzeix-Raviart element: application to elasticity, M2AN Math. Model. Numer. Anal., 37 (2003), 63-72.   DOI   ScienceOn
6 C.O. Horgan and L.E. Payne, On inequalities of Korn, Friedrichs and Babuska-Aziz, Arch. Rational Mech. Anal., 82 (1983), 165-179.
7 C.O. Horgan, Korn's inequalities and their applications in continuum mechanics, SIAM Rev., 37 (1995), 491-511.   DOI   ScienceOn
8 K.-Y. Kim, Guaranteed a posteriori error estimator for mixed finite element methods of linear elasticity with weak stress symmetry, submitted for publication.
9 M. Bebendorf, A note on the Poincare inequality for convex domains, Z. Anal. Anwendungen, 22 (2003), 751-756.
10 M. Ainsworth and J.T. Oden, A posteriori error estimation in finite element analysis, John Wiley and Sons, New York, 2000.
11 S. Ohnimus, E. Stein and E. Walhorn, Local error estimates of FEM for displacements and stresses in linear elasticity by solving local Neumann problems, Internat. J. Numer. Methods Engrg., 52 (2001), 727-746.   DOI   ScienceOn
12 K.-Y. Kim, Flux reconstruction for the P2 nonconforming finite element method with application to a posteriori error estimation, submitted for publication.