본문 바로가기
KERD
논문KCI 등재

Asymptotic exactness of some Bank-Weiser error estimator for quadratic triangular finite element

2

조회

0

다운로드

2

인용

0

참고문헌

키워드

주제분류수학

초록

We analyze a posteriori error estimator for the conforming $P2$ finite element on triangular meshes which is based on the solution of local Neumann problems. This error estimator extends the one for the conforming $P1$ finite element proposed in \cite{Bank-Weiser85}. We prove that it is asymptotically exact for the Poisson equation when the underlying triangulations are mildly structured and the solution is smooth enough.

Abstract

We analyze a posteriori error estimator for the conforming $P2$ finite element on triangular meshes which is based on the solution of local Neumann problems. This error estimator extends the one for the conforming $P1$ finite element proposed in \cite{Bank-Weiser85}. We prove that it is asymptotically exact for the Poisson equation when the underlying triangulations are mildly structured and the solution is smooth enough.

참고문헌 (20)

  1. Mark Ainsworth, "The influence and selection of subspaces for a posteriori error estimators", Numerische Mathematik, 73(4), pp.399~418 (1996), Springer Science and Business Media LLC[DOI]
  2. M. Ainsworth, "A posteriori error estimation in finite element analysis, Pure and Applied Mathematics (New York)" (2000), Wiley-Interscience
  3. A. Alonso, "Error estimators for a mixed method", Numerische Mathematik, 74(4), pp.385~395 (1996), Springer Science and Business Media LLC[DOI]
  4. R. E. Bank, "Some A Posteriori Error Estimators for Elliptic Partial Differential Equations", Mathematics of Computation, 44(170), pp.283~ (1985), JSTOR[DOI]
  5. Randolph E. Bank, "A Posteriori Error Estimates for the Stokes Problem", SIAM Journal on Numerical Analysis, 28(3), pp.591~623 (1991), Society for Industrial & Applied Mathematics (SIAM)[DOI]
  6. Randolph E. Bank, "Asymptotically Exact A Posteriori Error Estimators, Part I: Grids with Superconvergence", SIAM Journal on Numerical Analysis, 41(6), pp.2294~2312 (2003), Society for Industrial & Applied Mathematics (SIAM)[DOI]
  7. S. C. Brenner, "The mathematical theory of finite element methods" (2008), Springer
  8. R. Duran, "On the asymptotic exactness of Bank-Weiser's estimator", Numerische Mathematik, 62(1), pp.297~303 (1992), Springer Science and Business Media LLC[DOI]
  9. Yunqing Huang, "Superconvergence of quadratic finite elements on mildly structured grids", Mathematics of Computation, 77(263), pp.1253~1268 (2008), American Mathematical Society (AMS)[DOI]
  10. David Kay, "A Posteriori Error Estimation for Stabilized Mixed Approximations of the Stokes Equations", SIAM Journal on Scientific Computing, 21(4), pp.1321~1336 (1999), Society for Industrial & Applied Mathematics (SIAM)[DOI]
  11. Q. Liao, "Error estimation and stabilization for low order finite elements", Ph. D, pp.2010
  12. Qifeng Liao, "A simple yet effective a posteriori estimator for classical mixed approximation of Stokes equations", Applied Numerical Mathematics, 62(9), pp.1242~1256 (2012), Elsevier BV[DOI]
  13. Andrei Maxim, "Asymptotic exactness of an a posteriori error estimator based on the equilibrated residual method", Numerische Mathematik, 106(2), pp.225~253 (2007), Springer Science and Business Media LLC[DOI]
  14. Ahmed Naga, "A Posteriori Error Estimates Based on the Polynomial Preserving Recovery", SIAM Journal on Numerical Analysis, 42(4), pp.1780~1800 (2004), Society for Industrial & Applied Mathematics (SIAM)[DOI]
  15. Jeffrey S. Ovall, "Function, Gradient, and Hessian Recovery Using Quadratic Edge‐Bump Functions", SIAM Journal on Numerical Analysis, 45(3), pp.1064~1080 (2007), Society for Industrial & Applied Mathematics (SIAM)[DOI]
  16. R. Verfurth, "A posteriori error estimators for the Stokes equations", Numer. Math, 55(3), pp.309~325 (1989)
  17. R. Verfürth, "A posteriori error estimation and adaptive mesh-refinement techniques", Journal of Computational and Applied Mathematics, 50(1-3), pp.67~83 (1994), Elsevier BV[DOI]
  18. Haijun Wu, "Can We Have Superconvergent Gradient Recovery Under Adaptive Meshes?", SIAM Journal on Numerical Analysis, 45(4), pp.1701~1722 (2007), Society for Industrial & Applied Mathematics (SIAM)[DOI]
  19. Jinchao Xu, "Analysis of recovery type a posteriori error estimators for mildly structured grids", Mathematics of Computation, 73(247), pp.1139~1153 (2004), American Mathematical Society (AMS)[DOI]
  20. O. C. Zienkiewicz, "The superconvergent patch recovery anda posteriori error estimates. Part 1: The recovery technique", International Journal for Numerical Methods in Engineering, 33(7), pp.1331~1364 (1992), Wiley[DOI]

관련 논문AI추천

이 간행물의 다른 논문 (19건)