A comparison of a posteriori error estimators for mixed finite element discretizations by Raviart-Thomas elements

Mathematics of Computation

Volumn 68, Issue 228, 1999, Pages 1347-1378

  Wohlmuth, Barbara I ^a   Hoppe, Ronald H W ^a  

^a UNIVERSITY OF AUGSBURG   (Germany)

Author keywords

A posteriori error estimation; Adaptive grid refinement; Mixed finite elements

Indexed keywords

EID: 0033461695     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0025-5718-99-01125-4     Document Type: Article

References (59)

1. B. ACHCHAB, A. AGOUZAL, J. BARANGER, AND J. MAITRE, Estimateur d'erreur a posteriori hiérarchique. Application aux éléments finis mixtes, Numer. Math. 80 (1998), 159-179. CMP 49:01
2. B. ACHCHAB, A. AGOUZAL, J. BARANGER, AND J. MAITRE, Estimateur d'erreur a posteriori hiérarchique. Application aux éléments finis mixtes, Numer. Math. 80 (1998), 159-179. CMP 49:01
3. D. ARNOLD AND F. BREZZI, Mixed and nonconforming finite element methods: Implementation, post-processing and error estimates, RAIRO Modél. Math. Anal. Numér. 19 (1985), pp. 7-35. MR 87g:65176
4. D. ARNOLD AND F. BREZZI, Mixed and nonconforming finite element methods: Implementation, post-processing and error estimates, RAIRO Modél. Math. Anal. Numér. 19 (1985), pp. 7-35. MR 87g:65176
5. I. BABUŠKA AND W. RHEINBOLDT, Error estimates for adaptive finite element computations, SIAM J. Nurner. Anal., 15 (1978), pp. 736-754. MR 58:3400
6. I. BABUŠKA AND W. RHEINBOLDT, Error estimates for adaptive finite element computations, SIAM J. Nurner. Anal., 15 (1978), pp. 736-754. MR 58:3400
7. _, A posteriori error estimates for the finite element method, Int. J. Numer. Methods Eng., 12 (1978), pp. 1597-1615.
8. R. BANK, A. SHERMAN, AND A. WEISER, Refinement algorithm and data structures for regular local mesh refinement, in Scientific Computing, R. Stepleman et al., ed., vol. 44, IMACS North-Holland, Amsterdam, 1983, pp. 3-17. MR 85i:00014
9. R. BANK, A. SHERMAN, AND A. WEISER, Refinement algorithm and data structures for regular local mesh refinement, in Scientific Computing, R. Stepleman et al., ed., vol. 44, IMACS North-Holland, Amsterdam, 1983, pp. 3-17. MR 85i:00014
10. R. BANK AND A. WEISER, Some a posteriori error estimators for elliptic partial differential equations, Math. Comp., 44 (1985), pp. 283-301. MR 86g:65207
11. R. BANK AND A. WEISER, Some a posteriori error estimators for elliptic partial differential equations, Math. Comp., 44 (1985), pp. 283-301. MR 86g:65207
12. R. BECKER AND R. RANNACHER, Weighted a posteriori error control in FE methods, Tech. Report 96 - 1, SFB 359 - Universität Heidelberg, January 1996.
13. F. BORNEMANN, B. ERDMANN, AND R. KORNHUBER, A posteriori error estimates for elliptic problems in two and three spaces dimensions, SIAM J. Numer. Anal., 33 (1996), pp. 1188-1204 MR 98a:65161
14. F. BORNEMANN, B. ERDMANN, AND R. KORNHUBER, A posteriori error estimates for elliptic problems in two and three spaces dimensions, SIAM J. Numer. Anal., 33 (1996), pp. 1188-1204 MR 98a:65161
15. D. BRAESS, O. KLAAS, R. NIEKAMP, E. STEIN, AND F. WOBSCHAL, Error indicators for mixed finite elements in 2-dimensional linear elasticity, Comput. Methods Appl. Mech. Eng., 127, (1995), pp. 345-356 MR 96h:73045
16. D. BRAESS, O. KLAAS, R. NIEKAMP, E. STEIN, AND F. WOBSCHAL, Error indicators for mixed finite elements in 2-dimensional linear elasticity, Comput. Methods Appl. Mech. Eng., 127, (1995), pp. 345-356 MR 96h:73045
17. D. BRAESS AND R. VERFÜRTH, A posteriori error estimators for the Raviart-Thomas element, SIAM J. Numer. Anal., 33 (1996), pp. 2431-2444 MR 97m:65201
18. D. BRAESS AND R. VERFÜRTH, A posteriori error estimators for the Raviart-Thomas element, SIAM J. Numer. Anal., 33 (1996), pp. 2431-2444 MR 97m:65201
19. J. BRANDTS, Superconvergence and a posteriori error estimation for triangular mixed finite elements, Numer. Math., 68 (1994), pp. 311-324. MR 97a:65162
20. J. BRANDTS, Superconvergence and a posteriori error estimation for triangular mixed finite elements, Numer. Math., 68 (1994), pp. 311-324. MR 97a:65162
21. F. BREZZI AND M. FORTIN, Mixed and hybrid finite element methods, Springer-Verlag, New York, 1991. MR 92d:65187
22. F. BREZZI AND M. FORTIN, Mixed and hybrid finite element methods, Springer-Verlag, New York, 1991. MR 92d:65187
23. P. CLÉMENT, Approximation by finite element functions using local regularization, RAIRO Anal. Numér., 2 (1975), pp. 77-84. MR 53:4569
24. P. CLÉMENT, Approximation by finite element functions using local regularization, RAIRO Anal. Numér., 2 (1975), pp. 77-84. MR 53:4569
25. P. DEUFLHARD, P. LEINEN, AND H. YSERENTANT, Concepts of an adaptive hierarchical finite element code, IMPACT Comput. Sci. Engrg., 1 (1989), pp. 3-35.
26. R. DURAN AND R. RODRIGUEZ, On the asymptotic exactness of Bank-Weiser's estimator, Numer. Math., 62 (1992), pp. 297-303. MR 93e:65135
27. R. DURAN AND R. RODRIGUEZ, On the asymptotic exactness of Bank-Weiser's estimator, Numer. Math., 62 (1992), pp. 297-303. MR 93e:65135
28. K. ERIKSSON AND C. JOHNSON, An adaptive finite element method for linear elliptic problems, Math. Comput., 50 (1988), pp. 361-383.
29. R. EWING AND J. WANG, Analysis of multilevel decomposition iterative methods for mixed finite element methods, RAIRO Modél. Math. Anal. Numér. 28 (1994), pp. 377-398. MR 95e:65099
30. R. EWING AND J. WANG, Analysis of multilevel decomposition iterative methods for mixed finite element methods, RAIRO Modél. Math. Anal. Numér. 28 (1994), pp. 377-398. MR 95e:65099
31. R. HOPPE AND B. WOHLMUTH, Adaptive multilevel techniques for mixed finite element discretizations of elliptic boundary value problems, SIAM J. Numer. Anal., 34 (1997), pp. 1658-1681. MR 98e:65095
32. R. HOPPE AND B. WOHLMUTH, Adaptive multilevel techniques for mixed finite element discretizations of elliptic boundary value problems, SIAM J. Numer. Anal., 34 (1997), pp. 1658-1681. MR 98e:65095
33. _, Efficient numerical solution of mixed finite element discretizations by adaptive multilevel methods, Appl. Math., 40 (1995), pp. 227-248. MR 96b:65111
34. _, Efficient numerical solution of mixed finite element discretizations by adaptive multilevel methods, Appl. Math., 40 (1995), pp. 227-248. MR 96b:65111
35. _, Multilevel iterative solution and adaptive mesh refinement for mixed finite element discretizations, Appl. Num. Math., 23 (1997), pp. 97-117 MR 98g:65109
36. _, Multilevel iterative solution and adaptive mesh refinement for mixed finite element discretizations, Appl. Num. Math., 23 (1997), pp. 97-117 MR 98g:65109
37. _, Element-oriented and edge-oriented local error estimators for nonconforming finite element methods, RAIRO Modél. Math. Anal. Numér. 30 (1996), pp. 237-263. MR 97e:65124
38. _, Element-oriented and edge-oriented local error estimators for nonconforming finite element methods, RAIRO Modél. Math. Anal. Numér. 30 (1996), pp. 237-263. MR 97e:65124
39. C. JOHNSON, Numerical Solution of Partial Differential Equations by the Finite Element Method, no. 101, Cambridge University Press, Cambridge, 1987. MR 89b:65003a
40. C. JOHNSON, Numerical Solution of Partial Differential Equations by the Finite Element Method, no. 101, Cambridge University Press, Cambridge, 1987. MR 89b:65003a
41. C. JOHNSON AND P. HANSBO, Adaptive finite element methods in computational mechanics, Comp. Meth. Appl. Mech. Eng., 101 (1992), pp. 143-181. MR 93m:65157
42. C. JOHNSON AND P. HANSBO, Adaptive finite element methods in computational mechanics, Comp. Meth. Appl. Mech. Eng., 101 (1992), pp. 143-181. MR 93m:65157
43. R. RODRIGUEZ, Some remarks on the Zienkiewicz-Zhu estimator, Numer. Meth. for PDE, 10 (1994), pp. 625-636. MR 95e:65103
44. R. RODRIGUEZ, Some remarks on the Zienkiewicz-Zhu estimator, Numer. Meth. for PDE, 10 (1994), pp. 625-636. MR 95e:65103
45. T. STROUBOULIS AND J. ODEN, A posteriori error estimation of finite element approximations in fluid dynamics, Comp. Meth. Appl. Mech. Engrg., 78 (1990), pp. 201-242. MR 91a:76066
46. T. STROUBOULIS AND J. ODEN, A posteriori error estimation of finite element approximations in fluid dynamics, Comp. Meth. Appl. Mech. Engrg., 78 (1990), pp. 201-242. MR 91a:76066
47. B. SZABÓ AND I. BABUŠKA, Finite Element Analysis, Wiley, New York, 1991. MR 93f:73001
48. B. SZABÓ AND I. BABUŠKA, Finite Element Analysis, Wiley, New York, 1991. MR 93f:73001
49. R. VERFÜRTH, A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques, Wiley-Teubner, Chichester, 1996.
50. _, A posteriori error estimators for the Stokes equations, Numer. Math., 55 (1989), pp. 309-325. MR 90d:65187
51. _, A posteriori error estimators for the Stokes equations, Numer. Math., 55 (1989), pp. 309-325. MR 90d:65187
52. _, A posteriori error estimates for nonlinear problems. Finite element discretizations of elliptic equations, Math. Comput., 62 (1994), pp. 445-475. MR 94j:65136
53. _, A posteriori error estimates for nonlinear problems. Finite element discretizations of elliptic equations, Math. Comput., 62 (1994), pp. 445-475. MR 94j:65136
54. _, A posteriori error estimation and adaptive mesh-refinement techniques, J. Comp. Appl. Math., 50 (1994), pp. 67-83. MR 95c:65171
55. _, A posteriori error estimation and adaptive mesh-refinement techniques, J. Comp. Appl. Math., 50 (1994), pp. 67-83. MR 95c:65171
56. B. WOHLMUTH, Adaptive Multilevel-Finite-Elemente Methoden zur Lösung elliptischer Randwertprobleme, PhD thesis, TU München, 1995.
57. J. ZHU AND O. ZIENKIEWICZ, Adaptive techniques in the finite element method, Commun. Appl. Numer. Methods, 4 (1988), pp. 197-204.
58. O. ZIENKIEWICZ AND R. TAYLOR, The Finite Element Method, vol. 1, Mc Graw-Hill, London, 1989.
59. O. ZIENKIEWICZ AND J. ZHU, A simple error estimator and adaptive procedure for practical engineering analysis, J. Numer. Meth. Eng., 28 (1987), pp. 28-39.