Open Access
Volume 55, Number 5, September-October 2021
Page(s) 1921 - 1939
Published online 22 September 2021
  1. D.N. Arnold and F. Brezzi, Mixed and nonconforming finite element methods: implementation, postprocessing and error estimates. RAIRO: M2AN 19 (1985) 7–32. [Google Scholar]
  2. D.N. Arnold and R. Winther, Mixed finite elements for elasticity. Numer. Math. 92 (2002) 401–419. [Google Scholar]
  3. D.N. Arnold, J. Douglas Jr and C.P. Gupta, A family of higher order mixed finite element methods for plane elasticity. Numer. Math. 45 (1984) 1–22. [CrossRef] [MathSciNet] [Google Scholar]
  4. D.N. Arnold, G. Awanou and R. Winther, Finite elements for symmetric tensors in three dimensions. Math. Comput. 77 (2008) 1229–1251. [Google Scholar]
  5. E. Bänsch, Local mesh refinement in 2 and 3 dimensions. Impact Comput. Sci. Eng. 3 (1991) 181–191. [Google Scholar]
  6. R. Becker and S. Mao, An optimally convergent adaptive mixed finite element method. Numer. Math. 111 (2008) 35–54. [CrossRef] [MathSciNet] [Google Scholar]
  7. P. Binev, W. Dahmen and R. DeVore, Adaptive finite element methods with convergence rates. Numer. Math. 97 (2004) 219–268. [Google Scholar]
  8. S.C. Brenner, Korn’s inequalities for piecewise H1 vector fields. Math. Comput. 73 (2003) 1067–1087. [Google Scholar]
  9. S.C. Brenner and L. Ridgway Scott, The mathematical theory of finite element methods, 3 edition. In: Vol. 35 of Texts in Applied Mathematics. Springer, New York (2008). [Google Scholar]
  10. C. Carstensen, A unifying theory of a posteriori finite element error control. Numer. Math. 100 (2005) 617–637. [CrossRef] [MathSciNet] [Google Scholar]
  11. C. Carstensen and G. Dolzmann, A posteriori error estimates for mixed FEM in elasticity. Numer. Math. 81 (1998) 187–209. [Google Scholar]
  12. C. Carstensen and R.H.W. Hoppe, Error reduction and convergence for an adaptive mixed finite element method. Math. Comput. 75 (2006) 1033–1042. [CrossRef] [MathSciNet] [Google Scholar]
  13. C. Carstensen and H. Rabus, The adaptive nonconforming FEM for the pure displacement problem in linear elasticity is optimal and robust. SIAM J. Numer. Anal. 50 (2012) 1264–1283. [Google Scholar]
  14. C. Carstensen, M. Feischl, M. Page and D. Praetorius, Axioms of adaptivity. Comput. Math. Appl. 67 (2014) 1195–1253. [CrossRef] [PubMed] [Google Scholar]
  15. C. Carstensen, D. Gallistl and J. Gedicke, Residual-based a posteriori error analysis for symmetric mixed Arnold-Winther FEM. Numer. Math. 142 (2019) 205–234. [Google Scholar]
  16. J.M. Cascon, C. Kreuzer, R.H. Nochetto and K.G. Siebert, Quasi-optimal convergence rate for an adaptive finite element method. SIAM J. Numer. Anal. 46 (2008) 2524–2550. [Google Scholar]
  17. L. Chen, iFEM: an innovative finite element method package in Matlab. University of California Irvine, Technical report (2009). [Google Scholar]
  18. L. Chen, M. Holst and J. Xu, Convergence and optimality of adaptive mixed finite element methods. Math. Comput. 78 (2009) 35–53. [CrossRef] [Google Scholar]
  19. L. Chen, J. Hu and X. Huang, Fast auxiliary space preconditioners for linear elasticity in mixed form. Math. Comput. 78 (2018) 1601–1633. [Google Scholar]
  20. L. Chen, J. Hu, X. Huang and H. Man, Residual-based a posteriori error estimates for symmetric conforming mixed finite elements for linear elasticity problems. Sci. China Math. 61 (2018) 973–992. [Google Scholar]
  21. L. Diening, C. Kreuzer and R. Stevenson, Instance optimality of the adaptive maximum strategy. Found. Comput. Math. 16 (2016) 33–68. [CrossRef] [Google Scholar]
  22. W. Dörfler, A convergent adaptive algorithm for Poisson’s equation. SIAM J. Numer. Anal. 33 (1996) 1106–1124. [Google Scholar]
  23. M. Feischl, T. Führer and D. Praetorius, Adaptive FEM with optimal convergence rates for a certain class of nonsymmetric and possibly nonlinear problems. SIAM J. Numer. Anal. 52 (2014) 601–625. [CrossRef] [Google Scholar]
  24. V. Girault and L.R. Scott, Hermite interpolation of nonsmooth functions preserving boundary conditions. Math. Comput. 71 (2002) 1043–1074. [Google Scholar]
  25. S. Gong, S. Wu and J. Xu, New hybridized mixed methods for linear elasticity and optimal multilevel solvers. Numer. Math. 141 (2019) 569–604. [Google Scholar]
  26. P. Grisvard, Singularities in boundary value problems. In: Vol. 22 of Research in Applied Mathematics. Springer-Verlag, Berlin (1992). [Google Scholar]
  27. M. Holst, Y. Li, A. Mihalik and R. Szypowski, Convergence and optimality of adaptive mixed methods for Poisson’s equation in the FEEC framework. J. Comput. Math. 38 (2020) 748–767. [Google Scholar]
  28. J. Hu, Finite element approximations of symmetric tensors on simplicial grids in ℝn: the higher order case. J. Comput. Math. 33 (2015) 283–296. [Google Scholar]
  29. J. Hu and R. Ma, Partial relaxation of C0 vertex continuity of stresses of conforming mixed finite elements for the elasticity problem. Comput. Methods Appl. Math. 21 (2021) 89–108. [Google Scholar]
  30. J. Hu and S. Zhang, A family of conforming mixed finite elements for linear elasticity on triangular grids. Preprint arXiv:1406.7457 (2014). [Google Scholar]
  31. J. Huang and Y. Xu, Convergence and complexity of arbitrary order adaptive mixed element methods for the poisson equation. Sci. China Math. 55 (2012) 1083–1098. [Google Scholar]
  32. Y. Li, Some convergence and optimality results of adaptive mixed methods in finite element exterior calculus. SIAM J. Numer. Anal. 57 (2019) 2019–2042. [Google Scholar]
  33. Y. Li, Quasi-optimal adaptive mixed finite element methods for controlling natural norm errors. Math. Comput. 90 (2021) 565–593. [Google Scholar]
  34. Y. Li and L. Zikatanov, Nodal auxiliary a posteriori error estimates. Preprint arXiv:2010.06774 (2020). [Google Scholar]
  35. M. Lonsing and R. Verfürth, A posteriori error estimators for mixed finite element methods in linear elasticity. Numer. Math. 97 (2004) 757–778. [Google Scholar]
  36. W.F. Mitchell, A comparison of adaptive refinement techniques for elliptic problems. ACM Trans. Math. Softw. 15 (1989) 326–347. [CrossRef] [Google Scholar]
  37. J. Morgan and R. Scott, A nodal basis for C1 piecewise polynomials of degree n ≥ 5. Math. Comput. 29 (1975) 736–740. [Google Scholar]
  38. P. Morin, R.H. Nochetto and K.G. Siebert, Data oscillation and convergence of adaptive FEM. SIAM J. Numer. Anal. 38 (2000) 466–488. [CrossRef] [MathSciNet] [Google Scholar]
  39. R. Stevenson, Optimality of a standard adaptive finite element method. Found. Comput. Math. 7 (2007) 245–269. [CrossRef] [MathSciNet] [Google Scholar]
  40. R. Stevenson, The completion of locally refined simplicial partitions created by bisection. Math. Comput. 77 (2008) 227–241. [Google Scholar]
  41. R. Verfürth, A posteriori error estimation techniques for finite element methods. In: Numerical Mathematics and Scientific Computation. Oxford University Press, Oxford (2013). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you