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On the asymptotic exactness of an error estimator for the lowest-order Raviart-Thomas mixed finite element

김광연
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2013.09|한국수학논문집 (Korean Journal of Mathematics)|제21권 제3호|pp. 293-304|DOI http://dx.doi.org/10.11568/kjm.2013.21.3.293

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참고문헌

키워드

mixed finite element methoda posteriori error estimatorasymptotic exactnesssuperconvergence
주제분류수학

초록

In this paper we analyze an error estimator for the lowest-order triangular Raviart–Thomas mixed finite element which is based on solution of local problems for the error. This estimator was proposed in [Alonso, Error estimators for a mixed method, Numer. Math. 74 (1996), 385–395] and has a similar concept to that of Bank and Weiser. We show that it is asymptotically exact for the Poisson equation if the underlying triangulations are uniform and the exact solution is regular enough.

Abstract

In this paper we analyze an error estimator for the lowest-order triangular Raviart–Thomas mixed finite element which is based on solution of local problems for the error. This estimator was proposed in [Alonso, Error estimators for a mixed method, Numer. Math. 74 (1996), 385–395] and has a similar concept to that of Bank and Weiser. We show that it is asymptotically exact for the Poisson equation if the underlying triangulations are uniform and the exact solution is regular enough.

참고문헌 (18)

  1. M. Ainsworth, "A posteriori error estimation for lowest order Raviart-Thomas mixed finite elements", SIAM J. Sci. Comput., 30, pp.189~204 (2007)
  2. A. Alonso, "Error estimators for a mixed method", Numer. Math., 74, pp.385~395 (1996)
  3. R. E. Bank, "Some a posteriori error estimators for elliptic partial di erential equations", Math. Comp., 44, pp.283~301 (1985)
  4. D. Braess, "A posteriori error estimators for the Raviart-Thomas element", SIAM J. Numer. Anal., 33, pp.2431~2444 (1996)
  5. J. H. Brandts, "Superconvergence and a posteriori error estimation for trian- gular mixed finite elements", Numer. Math., 68, pp.311~324 (1994)
  6. F. Brezzi, "Mixed and hybrid nite element methods" (1991), Springer-Verlag
  7. C. Carstensen, "A posteriori error estimate for the mixed finite element method", Math. Comp., 66, pp.465~476 (1997)
  8. T. F. Dupont, "Superconvergence and postprocessing of uxes from lowest-order mixed methods on triangles and tetrahedra", SIAM J. Sci. Comput., 19, pp.1322~1332 (1998)
  9. R. Duran, "On the asymptotic exactness of Bank-Weiser's estimator", Numer. Math., 62, pp.297~303 (1992)
  10. K.-Y. Kim, "Guaranteed a posteriori error estimator for mixed nite element methods of elliptic problems", Appl. Math. Comp., 218, pp.11820~11831 (2012)
  11. M. G. Larson, "A posteriori error estimates for mixed nite element approximations of elliptic problems", Numer. Math, 108, pp.487~500 (2008)
  12. C. Lovadina, "Energy norm a posteriori error estimates for mixed nite element methods", Math. Comp., 75, pp.1659~1674 (2006)
  13. A. Maxim, "Asymptotic exactness of an a posteriori error estimator based on the equilibrated residual method", Numer. Math., 106, pp.225~253 (2007)
  14. P. A. Raviart, "A mixed finite element method for 2nd order elliptic problems, in Proc. Conf. on Mathematical Aspects of Finite Ele- ment Methods", Lecture Notes in Math., 606, pp.292~315 (1977), Springer-Verlag
  15. M. Vohralik, "A posteriori error estimates for lowest-order mixed finite ele- ment discretizations of convection-diffusion-reaction equations", SIAM J. Numer. Anal., 45, pp.1570~1599 (2007)
  16. B. I. Wohlmuth, "A comparison of a posteriori error estimators for mixed nite element discretizations by Raviart-Thomas elements", Math. Comp., 68, pp.1347~1378 (1999)
  17. J. Xu, "Analysis of recovery type a posteriori error estimators for mildly structured grids", Math. Comp., 73, pp.1139~1152 (2004)
  18. N. Yan, "Gradient recovery type a posteriori error estimates for finite element approximations on irregular meshes", Comput. Methods Appl. Mech. Engrg., 190, pp.4289~4299 (2001)

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