참고문헌
- M. Ainsworth, The influence and selection of subspaces for a posteriori error estimators, Numer. Math. 73 (1996), no. 4, 399-418. https://doi.org/10.1007/s002110050198
- M. Ainsworth and J. T. Oden, A posteriori error estimation in finite element analysis, Pure and Applied Mathematics (New York), Wiley-Interscience, New York, 2000. https://doi.org/10.1002/9781118032824
- A. Alonso, Error estimators for a mixed method, Numer. Math. 74 (1996), no. 4, 385-395. https://doi.org/10.1007/s002110050222
- R. E. Bank and A. Weiser, Some a posteriori error estimators for elliptic partial differential equations, Math. Comp. 44 (1985), no. 170, 283-301. https://doi.org/10.2307/ 2007953
- R. E. Bank and B. D. Welfert, A posteriori error estimates for the Stokes problem, SIAM J. Numer. Anal. 28 (1991), no. 3, 591-623. https://doi.org/10.1137/0728033
- R. E. Bank and J. Xu, Asymptotically exact a posteriori error estimators. I. Grids with superconvergence, SIAM J. Numer. Anal. 41 (2003), no. 6, 2294-2312. https://doi.org/10.1137/S003614290139874X
- S. C. Brenner and L. R. Scott, The mathematical theory of finite element methods, third edition, Texts in Applied Mathematics, 15, Springer, New York, 2008. https://doi.org/10.1007/978-0-387-75934-0
- R. Duran and R. Rodrguez, On the asymptotic exactness of Bank-Weiser's estimator, Numer. Math. 62 (1992), no. 3, 297-303. https://doi.org/10.1007/BF01396231
- Y. Huang and J. Xu, Superconvergence of quadratic finite elements on mildly structured grids, Math. Comp. 77 (2008), no. 263, 1253-1268. https://doi.org/10.1090/S0025-5718-08-02051-6
- D. Kay and D. Silvester, A posteriori error estimation for stabilized mixed approximations of the Stokes equations, SIAM J. Sci. Comput. 21 (1999/00), no. 4, 1321-1336. https://doi.org/10.1137/S1064827598333715
- Q. Liao, Error estimation and stabilization for low order nite elements, Ph.D thesis, The University of Manchester, 2010.
- Q. Liao and D. Silvester, A simple yet effective a posteriori estimator for classical mixed approximation of Stokes equations, Appl. Numer. Math. 62 (2012), no. 9, 1242-1256. https://doi.org/10.1016/j.apnum.2010.05.003
- A. Maxim, Asymptotic exactness of an a posteriori error estimator based on the equilibrated residual method, Numer. Math. 106 (2007), no. 2, 225-253. https://doi.org/10.1007/s00211-007-0064-3
- A. Naga and Z. Zhang, A posteriori error estimates based on the polynomial preserving recovery, SIAM J. Numer. Anal. 42 (2004), no. 4, 1780-1800. https://doi.org/10.1137/S0036142903413002
- J. S. Ovall, Function, gradient, and Hessian recovery using quadratic edge-bump functions, SIAM J. Numer. Anal. 45 (2007), no. 3, 1064-1080. https://doi.org/10.1137/060648908
- R. Verfurth, A posteriori error estimators for the Stokes equations, Numer. Math. 55 (1989), no. 3, 309-325. https://doi.org/10.1007/BF01390056
- R. Verfurth, A posteriori error estimation and adaptive mesh-refinement techniques, J. Comput. Appl. Math. 50 (1994), no. 1-3, 67-83. https://doi.org/10.1016/0377-0427(94)90290-9
- H. Wu and Z. Zhang, Can we have superconvergent gradient recovery under adaptive meshes?, SIAM J. Numer. Anal. 45 (2007), no. 4, 1701-1722. https://doi.org/10.1137/060661430
- J. Xu and Z. Zhang, Analysis of recovery type a posteriori error estimators for mildly structured grids, Math. Comp. 73 (2004), no. 247, 1139-1152. https://doi.org/10.1090/S0025-5718-03-01600-4
- O. C. Zienkiewicz and J. Z. Zhu, The superconvergent patch recovery and a posteriori error estimates. I. The recovery technique, Internat. J. Numer. Methods Engrg. 33 (1992), no. 7, 1331-1364. https://doi.org/10.1002/nme.1620330702