Element-oriented and edge-oriented local error estimators for nonconforming finite element methods

Ronald H. W. Hoppe; Barbara Wohlmuth

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1996)

  • Volume: 30, Issue: 2, page 237-263
  • ISSN: 0764-583X

How to cite

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Hoppe, Ronald H. W., and 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 30.2 (1996): 237-263. <http://eudml.org/doc/193804>.

@article{Hoppe1996,
author = {Hoppe, Ronald H. W., Wohlmuth, Barbara},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {nonconforming finite element; error estimators; numerical results},
language = {eng},
number = {2},
pages = {237-263},
publisher = {Dunod},
title = {Element-oriented and edge-oriented local error estimators for nonconforming finite element methods},
url = {http://eudml.org/doc/193804},
volume = {30},
year = {1996},
}

TY - JOUR
AU - Hoppe, Ronald H. W.
AU - Wohlmuth, Barbara
TI - Element-oriented and edge-oriented local error estimators for nonconforming finite element methods
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1996
PB - Dunod
VL - 30
IS - 2
SP - 237
EP - 263
LA - eng
KW - nonconforming finite element; error estimators; numerical results
UR - http://eudml.org/doc/193804
ER -

References

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  1. [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. Zbl0567.65078MR813687
  2. [2] R. E. BANK, 1990, PLTMG - A software package for solving elliptic partial differential equations, User's Guide 6.0., SIAM, Philadelphia. Zbl0717.68001MR1052151
  3. [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. MR751598
  4. [4] R. E. BANK and A. WEISER, 1985, Some posteriori error estimators for elliptic partial differential equations. Math. Comp., 44, pp. 283-301. Zbl0569.65079MR777265
  5. [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. [6] J. H. BRAMBLE, J. E. PASCIAK, J. XU, 1990, Parallel multilevel preconditioners. Math. Comp., 55, pp. 1-22. Zbl0703.65076MR1023042
  7. [7] F. BREZZI and M. FORTIN, 1991, Mixed and hybrid finite element methods, Springer, Berlin-Heidelberg-New York. Zbl0788.73002MR1115205
  8. [8] P. G. CLARLET, 1978, The finite element method for elliptic problems, North-Holland, Amsterdam. Zbl0383.65058MR520174
  9. [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. Zbl0706.65111
  10. [10] P. OSWALD, 1991, On a BPX-preconditioner for PI elements, Prepint, FSU Jena. Zbl0787.65018
  11. [11] B. SZABÓ and I. BABU&#0160;KA, 1991, Finite element analysis, John Wiley & Sons, New York. 
  12. [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. [13] J. XU, 1989, Theory of multilevel methods, Department of Mathematics Pennstate, Report No. AM 48. 
  14. [14] H. YSERENTANT, 1990, Two preconditioners based on the multilevel splitting of finite element spaces, Numer. Math, 58, pp. 163-184. Zbl0708.65103MR1069277

Citations in EuDML Documents

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  1. Michael Hintermüller, Ronald H.W. Hoppe, Yuri Iliash, Michael Kieweg, An error analysis of adaptive finite element methods for distributed elliptic control problems with control constraints
  2. Michael Kieweg, Yuri Iliash, Ronald H. W. Hoppe, Michael Hintermüller, An a posteriori error analysis of adaptive finite element methods for distributed elliptic control problems with control constraints
  3. Carsten Carstensen, Quasi-interpolation and a posteriori error analysis in finite element methods
  4. Friedhelm Schieweck, Error Estimates with Post-Processing for Nonconforming Finite Elements
  5. Rudi Beck, Ralf Hiptmair, Ronald H. W. Hoppe, Barbara Wohlmuth, Residual based a posteriori error estimators for eddy current computation
  6. Friedhelm Schieweck, A posteriori error estimates with post-processing for nonconforming finite elements
  7. Erik Burman, Alexandre Ern, A continuous finite element method with face penalty to approximate Friedrichs' systems
  8. Rudi Beck, Ralf Hiptmair, Ronald H.W. Hoppe, Barbara Wohlmuth, Residual based a posteriori error estimators for eddy current computation
  9. Linda El Alaoui, Alexandre Ern, Residual and hierarchical a posteriori error estimates for nonconforming mixed finite element methods
  10. Linda El Alaoui, Alexandre Ern, Residual and hierarchical error estimates for nonconforming mixed finite element methods

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