Element-oriented and edge-oriented local error estimators for nonconforming finite element methods
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 30 (1996) no. 2, p. 237-263
@article{M2AN_1996__30_2_237_0,
     author = {Hoppe, Ronald H. W. and Wohlmuth, Barbara},
     title = {Element-oriented and edge-oriented local error estimators for nonconforming finite element methods},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {Dunod},
     volume = {30},
     number = {2},
     year = {1996},
     pages = {237-263},
     zbl = {0843.65075},
     mrnumber = {1382112},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1996__30_2_237_0}
}
Hoppe, Ronald H. W.; Wohlmuth, Barbara. Element-oriented and edge-oriented local error estimators for nonconforming finite element methods. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 30 (1996) no. 2, pp. 237-263. http://www.numdam.org/item/M2AN_1996__30_2_237_0/

[1] D. N. Arnold and F. Brezzi, 1985, Mixed and nonconforming finite element methods : implementation, post-processing and error estimates, Math. Modelling Numer. Anal., 19, pp.7-35. | Numdam | MR 813687 | Zbl 0567.65078

[2] R. E. Bank, 1990, PLTMG - A software package for solving elliptic partial differential equations, User's Guide 6.0., SIAM, Philadelphia. | MR 1052151 | Zbl 0717.68001

[3] R. E. Bank, A. H. Sherman and A. Weiser, 1983, Refinement algorithm and data structures for regular local mesh refinement, Scientific Computing, R. Stepleman et al. (eds.), Amsterdam, IMACS North-Holland, pp. 3-17. | MR 751598

[4] R. E. Bank and A. Weiser, 1985, Some posteriori error estimators for elliptic partial differential equations. Math. Comp., 44, pp. 283-301. | MR 777265 | Zbl 0569.65079

[5] F. Bornemann, 1991, A sharpened condition number estimate for the BPX preconditioner of elliptic finite element problems on highly nonuniform triangulations, Konrad-Zese-Zentruman Berlin, Prepint SC 91-9.

[6] J. H. Bramble, J. E. Pasciak, J. Xu, 1990, Parallel multilevel preconditioners. Math. Comp., 55, pp. 1-22. | MR 1023042 | Zbl 0703.65076

[7] F. Brezzi and M. Fortin, 1991, Mixed and hybrid finite element methods, Springer, Berlin-Heidelberg-New York. | MR 1115205 | Zbl 0788.73002

[8] P. G. Clarlet, 1978, The finite element method for elliptic problems, North-Holland, Amsterdam. | MR 520174 | Zbl 0383.65058

[9] P. Deuflhard, P. Leinen and H. Yserentant, 1989, Concepts of an adaptive hierarchical finite element code, IMPACT comut. Sci. Engrg., 1, pp. 3-35. | Zbl 0706.65111

[10] P. Oswald, 1991, On a BPX-preconditioner for PI elements, Prepint, FSU Jena. | Zbl 0787.65018

[11] B. Szabó and I. Babu Ka, 1991, Finite element analysis, John Wiley & Sons, New York.

[12] B. Wohlmuth and R. H. W. Hoppe, 1994, Multilevel approaches to nonconforming finite element discretizations of linear second order elliptic boundary value problems, to appear in Journal of Computation and Information, 4, pp. 73-86.

[13] J. Xu, 1989, Theory of multilevel methods, Department of Mathematics Pennstate, Report No. AM 48.

[14] H. Yserentant, 1990, Two preconditioners based on the multilevel splitting of finite element spaces, Numer. Math, 58, pp. 163-184. | MR 1069277 | Zbl 0708.65103