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A posteriori error estimators for nonconforming finite element methods. (English) Zbl 0853.65110
The authors introduce two a posteriori error estimators for piecewise linear nonconforming finite element approximation of second-order elliptic problems. They prove that these estimators are equivalent to the energy norm of the error. Finally, they present several numerical experiments showing the good behavior of the estimators when they are used as local error indicators for adaptive refinement.

MSC:
65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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[1] D. N. ARNOLD, F. BREZZI, Mixed and nonconforming finite element method simplementation, postprocessing and error estimates, R.A.I.R.O., Modél. Math. Anal Numer. 19, 1985, pp. 7-32. Zbl0567.65078 MR813687 · Zbl 0567.65078
[2] D. N. ARNOLD, R. S. FALK, A uniformly accurate finite element method for the Reissner-Mindlin plate. SIAM J. Numer. Anal. 26, 1989, pp. 1276-1290. Zbl0696.73040 MR1025088 · Zbl 0696.73040
[3] I. BABUŠKA, R. DURÁN, R. RODRÍGUEZ, Analysis of the efficiency of an a posteriori error estimator for liner triangular finite elements, Siam J. Numer. Anal. 29, 1992, pp. 947-964. Zbl0759.65069 MR1173179 · Zbl 0759.65069
[4] I. BABUŠKA, A. MILLER, A feedback finite element method with a posteriori error estimation. Part I : The finite element method and some basic properties of the a posteriori error estimator, Comp. Meth. Appl. Mech. Eng. 61, 1987, pp. 1-40. Zbl0593.65064 MR880421 · Zbl 0593.65064
[5] I. BABUŠKA, W. C. RHEINBOLDT, A posteriori error estimators in the finite element method, Inter. J. Numer. Meth. Eng. 12, 1978, pp. 1587-1615. Zbl0396.65068 · Zbl 0396.65068
[6] R. E. BANK, A. WEISER, Some a posteriori error estimators for elliptic partial differential equations, Math. Comp. 44, 1985,, pp. 283-301. Zbl0569.65079 MR777265 · Zbl 0569.65079
[7] P. G. CIARLET, The finite element method for elliptic problems, North Holland, 1978. Zbl0383.65058 MR520174 · Zbl 0383.65058
[8] D. F. GRIFFITHS, A. R. MITCHELL, Nonconforming elements, The mathematical basis of finite element methods, D. F. Griffiths, ed., Clarendon Press, Oxford, 1984, pp. 41-69. MR807009
[9] L. D. MARINI, An inexpensive method for the evaluation of the solution of the lowest order Raviart-Thomas mixed method, SIAM J. Numer. Anal. 22, 1985, pp. 493-496. Zbl0573.65082 MR787572 · Zbl 0573.65082
[10] M. C. RIVARA, Mesh refinement processes based on the generalized bisection of simplices, SIAM J. Numer. Anal. 21, 1984, pp.604-613 Zbl0574.65133 MR744176 · Zbl 0574.65133
[11] L. R. SCOTT, S. SHANG, Finite element interpolation of non-smooth functions satisfying boundary conditions, Math. Comp. 54, 1990, pp. 483-493. Zbl0696.65007 MR1011446 · Zbl 0696.65007
[12] R. VERFÜRTH, A posteriori error estimators for the Stokes equations, Numer.Math. 55, 1989, pp. 309-325. Zbl0674.65092 MR993474 · Zbl 0674.65092
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