Asymptotic exactness of some Bank-Weiser error estimator for quadratic triangular finite element
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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)
- 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]
- M. Ainsworth, "A posteriori error estimation in finite element analysis, Pure and Applied Mathematics (New York)" (2000), Wiley-Interscience
- A. Alonso, "Error estimators for a mixed method", Numerische Mathematik, 74(4), pp.385~395 (1996), Springer Science and Business Media LLC[DOI]
- R. E. Bank, "Some A Posteriori Error Estimators for Elliptic Partial Differential Equations", Mathematics of Computation, 44(170), pp.283~ (1985), JSTOR[DOI]
- 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]
- 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]
- S. C. Brenner, "The mathematical theory of finite element methods" (2008), Springer
- 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]
- 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]
- 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]
- Q. Liao, "Error estimation and stabilization for low order finite elements", Ph. D, pp.2010
- 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]
- 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]
- 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]
- 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]
- R. Verfurth, "A posteriori error estimators for the Stokes equations", Numer. Math, 55(3), pp.309~325 (1989)
- 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]
- 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]
- 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]
- 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]
