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. Daniela Capatina-Papaghiuc, Nicolas Raynaud, Numerical approximation of stiff transmission problems by mixed finite element methods
  2. Ronald H. W. Hoppe, Barbara Wohlmuth, Element-oriented and edge-oriented local error estimators for nonconforming finite element methods
  3. E. Dari, R. Duran, C. Padra, V. Vampa, A posteriori error estimators for nonconforming finite element methods
  4. Francesca Gardini, Mixed approximation of eigenvalue problems: A superconvergence result
  5. Riccardo Sacco, Fabio Manganini, Joseph W. Jerome, Modeling and Simulation of Thermo-Fluid-Electrochemical Ion Flow in Biological Channels
  6. Marian Slodička, Error estimates of an efficient linearization scheme for a nonlinear elliptic problem with a nonlocal boundary condition
  7. Zhangxin Chen, Analysis of mixed methods using conforming and nonconforming finite element methods
  8. Marian Slodička, Error estimates of an efficient linearization scheme for a nonlinear elliptic problem with a nonlocal boundary condition
  9. Marián Slodička, Recovery of an unknown flux in parabolic problems with nonstandard boundary conditions: Error estimates
  10. Paola Causin, Riccardo Sacco, Carlo L. Bottasso, Flux-upwind stabilization of the discontinuous Petrov–Galerkin formulation with Lagrange multipliers for advection-diffusion problems

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