Analysis of the superconvergent patch recovery technique and a posteriori error estimator in the finite element method (II)

Computer Methods in Applied Mechanics and Engineering

Volumn 163, Issue 1-4, 1998, Pages 159-170

  Zhang, Zhimin ^a   Zhu, J Z ^b  

^a TEXAS TECH UNIVERSITY   (United States)

^b UES Software Inc   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY VALUE PROBLEMS; CONVERGENCE OF NUMERICAL METHODS; FINITE ELEMENT METHOD; LEAST SQUARES APPROXIMATIONS; PROBLEM SOLVING; TENSORS;

A POSTERIOR ERROR ESTIMATOR; SUPERCONVERGENT PATCH RECOVERY TECHNIQUE;

ERROR ANALYSIS;

EID: 0032154296     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(98)00010-3     Document Type: Article

References (23)

1. [1] O.C. Zienkiewicz and J.Z. Zhu, The superconvergence patch recovery and a posteriori error estimates. Part 1: The recovery technique, Int. J. Numer. Methods Engrg. 33 (1992) 1331-1364.
2. [2] O.C. Zienkiewicz and J.Z. Zhu, The superconvergence patch recovery and a posteriori error estimates. Part 2: Error estimates and adaptivity, Int. J. Numer. Methods Engrg. 33 (1992) 1365-1382.
3. [3] O.C. Zienkiewicz and J.Z. Zhu, The superconvergence patch recovery (SPR) and adaptive finite element refinement. Comput. Methods Appl. Mech. Engrg. 101 (1992) 207-224.
4. [4] Z. Zhang and J.Z. Zhu, Analysis of the superconvergent patch recovery technique and a posteriori error estimator in the finite element method (I), Comput. Methods Appl. Mech. Engrg. 123 (1995) 173-187.
5. [5[ J.T. Oden and H.J. Brauchli, On the calculation of consistent stress distributions in finite element applications, Int. J. Numer. Methods Engrg. 3 (1971) 317-325.
6. [6] E. Hinton and J.S. Campbell, Local and global smoothing of discontinuous finite element functions using a least square method, Int. J. Numer. Methods Engrg. 8 (1974) 461-480.
7. [7] M. Zlámal, Superconvergence and reduced integration in the finite element method, Math. Comput. 32 (1977) 663-685.
8. [8] J.H. Bramble and A.H. Schatz, Higher order local accuracy by averaging in the finite element method, Math. Comput. 31 (1977) 74-111.
9. [9] N.D. Levine, Superconvergent recovery of the gradient from piecewise linear finite element approximations, IMA J. Numer. Anal. 5 (1985) 407-427.
10. [10] M.F. Wheeler and J.R. Whiteman, Superconvergent recovery of gradients on subdomains from piecewise linear finite element approximations, Numer. Methods for PDEs 3 (1987) 65-82.
11. [11] A.B. Andreev and R.D. Lazarov, Superconvergence of the gradient for quadratic triangular finite element methods, Numer. Methods for PDEs 4 (1988) 15-32.
12. [12] M.T. Nakao, Superconvergence of the gradient of Galerkin approximations for elliptic problems, RAIRO Modél. Math. Anal. Numér. 21 (1987) 679-695.
13. [13] M. Křížek and P. Neittaanmäki, On Superconvergence techniques, Acta Appl. Math. 9 (1987) 175-198.
14. [14] J. Douglas Jr. and T. Dupont, Superconvergence for Galerkin methods for the two point boundary problem via local projections, Numer. Math. 21 (1973) 270-278.
15. [15] M.F. Wheeler, An optimal L∝ error estimate for Galerkin approximations of solutions of two point boundary value problems, SIAM Numer. Anal. 10 (1973) 914-917.
16. [16] J. Douglas Jr., T. Dupont and M.F. Wheeler, An L∝ estimate and superconvergence result for a Galerkin method for ellipetic equations based on tensor products of piecewise polynomials, RAIRO Anal. Numer. 8 (1974) 61-66.
17. [17] C.M. Chen, Superconvergent points of Galerkin's method for two point boundary value problems, J. Numer. Anal. Chinese Univ. 1 (1979) 73-79.
18. [18] R.E. Ewing, R.D. Lazarov and J. Wang, Superconvergence of the velocity along the gauss lines in mixed finite element methods, SIAM J. Numer. Anal. 28 (1991) 1015-1029.
19. [19] Q.D. Zhu and Q. Lin, Superconvergence Theory of the Finite Element Method (Human Science Press, China, 1989).
20. [20] L.B. Wahlbin, Local behavior in finite element methods, in: P.G. Ciarlet and J.L. Lions, eds., Handbook of Numerical Analysis, Vol. II, Finite Element Methods (Part 1) (Elsevier Science Publishers B.V., North-Holland, 1991) 353-522.
21. [21] L.B, Wahlbin, Superconvergence in Galerkin Finite Element Methods, Lecture Notes in Mathematics, Vol. 1605 (Springer, Berlin, 1995).
22. [22] N.N. Lebedev, Special Functions & Their Applications (Dover, 1972).
23. [23] P.G. Ciarlet, The Finite Element Method for Elliptic Problems (North-Holland, Amsterdam, 1978).