Mixed and nonconforming finite element methods : implementation, postprocessing and error estimates

D. N. Arnold; F. Brezzi

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1985)

  • Volume: 19, Issue: 1, page 7-32
  • ISSN: 0764-583X

How to cite

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Arnold, D. N., and Brezzi, F.. "Mixed and nonconforming finite element methods : implementation, postprocessing and error estimates." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 19.1 (1985): 7-32. <http://eudml.org/doc/193443>.

@article{Arnold1985,
author = {Arnold, D. N., Brezzi, F.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {nonconforming finite element methods; mixed finite elements; Lagrange multipliers; Raviart-Thomas methods; Hellan-Herrmann-Johnson method for biharmonic problems; Morley method},
language = {eng},
number = {1},
pages = {7-32},
publisher = {Dunod},
title = {Mixed and nonconforming finite element methods : implementation, postprocessing and error estimates},
url = {http://eudml.org/doc/193443},
volume = {19},
year = {1985},
}

TY - JOUR
AU - Arnold, D. N.
AU - Brezzi, F.
TI - Mixed and nonconforming finite element methods : implementation, postprocessing and error estimates
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1985
PB - Dunod
VL - 19
IS - 1
SP - 7
EP - 32
LA - eng
KW - nonconforming finite element methods; mixed finite elements; Lagrange multipliers; Raviart-Thomas methods; Hellan-Herrmann-Johnson method for biharmonic problems; Morley method
UR - http://eudml.org/doc/193443
ER -

References

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  2. [2] I BABUSKA, J OSBORN and J PITKARANTA, Analysis of mixed methods using mesh dependent norms, Math Comput 35 (1980), 1039-1062 Zbl0472.65083MR583486
  3. [3] A BENSOUSSON, J L LIONS, G PAPANICOLAU, Asymptotic Analysis of Periodic Structures, North-Holland, Amsterdam, 1978 Zbl0404.35001MR503330
  4. [4] F BREZZI and P A RAVIART, Mixed finite element methods for 4th order elliptic equations, in Proc of the Royal Irish Academy Conference on Numerical Analysis, Academic Press, London, 1977 Zbl0434.65085MR657975
  5. [5] P G CIARLET, The Finite Element Method for Elliptic Equations, North-Holland, Amsterdam, 1978 Zbl0383.65058MR520174
  6. [6] J DOUGLAS and J E ROBERTS, Global estimates for mixed methods for second order elliptics, to appear in Math Comput Zbl0624.65109
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  8. [8] B FRAEJIS DE VEUBEKE, Displacement and equilibrium models in the finite element method, in Stress Analysis, O C Zienkiewicz and G Holister, eds , Wiley, New York, 1965 
  9. [9] K HELLAN, Analysis of elastic plates in flexure by a simplified finite element method, Acta Polytechnica Scandinavica, Ci 46, Trondheim, 1967 Zbl0237.73046
  10. [10] L HERRMANN, Finite element bending analysis for plates, J Eng Mech Div ASCE, a 3, EM5 (1967), 49-83 
  11. [11] P LASCAUX and P LESAINT, Some nonconforming finite elements for the plate bending problem, R A I R O Anal numer 9 (1975), 9-53 Zbl0319.73042MR423968
  12. [12] C JOHNSON, On the convergence of a mixed finite element method for plate bending problems, Numer Math 21 (1973), 43-62 Zbl0264.65070MR388807
  13. [13] L S D MORLEY, The triangular equilibrium element in the solution of plate bending problems, Aero Quart 19 (1968), 149-169 
  14. [14] R RANNACHER, Nonconforming finite element methods for eigenvalue problems in linear plate theory, Numer Math 33 (1979), 23-42 Zbl0394.65035MR545740
  15. [15] R RANNACHER, On nonconforming and mixed finite elements for plate bending problems The linear case R A I R O Anal numer 13 (1979), 369-387 Zbl0425.35042MR555385
  16. [16] P A RAVIART and J M THOMAS, A mixed finite element method for second order elliptic problems in Mathematical Aspects of the Finite Element Method, Lecture Notes in Mathematics 606, Springer-Verlag, Berlin, 1977 Zbl0362.65089MR483555

Citations in EuDML Documents

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  1. Paola Causin, Formulazioni ad elementi finiti misti-ibridi di tipo Galerkin e Petrov-Galerkin in meccanica dei continui
  2. Daniela Capatina-Papaghiuc, Nicolas Raynaud, Numerical approximation of stiff transmission problems by mixed finite element methods
  3. Ronald H. W. Hoppe, Barbara Wohlmuth, Element-oriented and edge-oriented local error estimators for nonconforming finite element methods
  4. E. Dari, R. Duran, C. Padra, V. Vampa, A posteriori error estimators for nonconforming finite element methods
  5. Riccardo Sacco, Fabio Manganini, Joseph W. Jerome, Modeling and Simulation of Thermo-Fluid-Electrochemical Ion Flow in Biological Channels
  6. Xuefeng Liu, Fumio Kikuchi, Explicit estimation of error constants appearing in non-conforming linear triangular finite element method
  7. Francesca Gardini, Mixed approximation of eigenvalue problems: A superconvergence result
  8. Marian Slodička, Error estimates of an efficient linearization scheme for a nonlinear elliptic problem with a nonlocal boundary condition
  9. Zhangxin Chen, Analysis of mixed methods using conforming and nonconforming finite element methods
  10. Marián Slodička, Recovery of an unknown flux in parabolic problems with nonstandard boundary conditions: Error estimates

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