On the numerical solution of the first biharmonic equation

P. Peisker

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1988)

  • Volume: 22, Issue: 4, page 655-676
  • ISSN: 0764-583X

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Peisker, P.. "On the numerical solution of the first biharmonic equation." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 22.4 (1988): 655-676. <http://eudml.org/doc/193545>.

@article{Peisker1988,
author = {Peisker, P.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {biharmonic equation; mixed finite element method; method of conjugate gradients; convergence; condition number; precondition},
language = {eng},
number = {4},
pages = {655-676},
publisher = {Dunod},
title = {On the numerical solution of the first biharmonic equation},
url = {http://eudml.org/doc/193545},
volume = {22},
year = {1988},
}

TY - JOUR
AU - Peisker, P.
TI - On the numerical solution of the first biharmonic equation
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1988
PB - Dunod
VL - 22
IS - 4
SP - 655
EP - 676
LA - eng
KW - biharmonic equation; mixed finite element method; method of conjugate gradients; convergence; condition number; precondition
UR - http://eudml.org/doc/193545
ER -

References

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  1. [1] O. AXELSSON and V. A. BARKER, Finite Element Solution of Boundary Value Problems, Theory and Computation. Academic Press 1984. Zbl0537.65072MR758437
  2. [2] P. E. BJØRSTAD, Fast numerical solution of the biharmonic Dirichlet problem on rectangles, Siam J. Numer. Anal. 20, 59-71 (1983). Zbl0561.65077MR687367
  3. [3] J. F. BOURGAT, Numerical study of a dual iterative method for solving a finite element approximation of the biharmonic equation, Comput. Methods Appl. Mech. 9, 203-218 (1976). Zbl0335.65052MR431743
  4. [4] D. BRAESS and P. PEISKER, On the numerical solution of the biharmonic equation and the role of squaring matrices for preconditioning, IMA Journal of Numerical Analysis 6, 393-404 (1986). Zbl0616.65108MR968266
  5. [5] P. G. CIARLET, The Finite Element Method for Elliptic Problems, North Holland 1978. Zbl0383.65058MR520174
  6. [6] P. G. CIARLET and R. GLOWINSKI, Dual iterative techniques for solving a finite element approximation of the biharmonic equation, Comput. Methods Appl. Mech. 5, 277-295 (1975). Zbl0305.65068MR373321
  7. [7] L. W. EHRLICH, Solving the biharmonic equation as a coupled difference equation, Siam J. Numer. Anal. 8, 278-287 (1971). Zbl0215.55702MR288972
  8. [8] R. GLOWINSKI and O. PIRONNEAU, Numerical methods for the first biharmonic equation and for the two dimensional Stokes problem, Siam Rev., 167-212 (1979). Zbl0427.65073MR524511
  9. [9] W. HACKBUSCH, Multi-Grid Methods and Applications, Springer Berlin-Heidelberg-New York, Heidelberg 1985. Zbl0595.65106
  10. [10] J. L. LIONS, E. MAGENES, Non-Homogeneous Boundary Value Problems and Applications I, Springer Berlin-Heidelberg-New York 1972. Zbl0223.35039
  11. [11] P. PEISKER, Zwei numerische Verfahren zur Lösung der biharmonischen Gleichung unter besonderer Berücksichtigung der Mehrgitteridee, Dissertation, Bochum 1985. Zbl0573.65085
  12. [12] J. PITKÄRANTA, Boundary subspaces for the finite element method with Lagrange multipliers, Numer. Math. 33, 273-289 (1979). Zbl0422.65062MR553590
  13. [13] R. VERFÜRTH, Error estimates for a mixed finite element approximation of the Stokes equations, R.A.I.R.O. Numerical Analysis 18, 175-182 (1984). Zbl0557.76037MR743884
  14. [14] O. B. WIDLUND, Iterative methods for elliptic problems partitioned into substructures and the biharmonic Dirichlet problem, in : Proceedings of the sixth international conference on computing methods in science and engineering held at Versailles, France, December, 12-16, 1983. Zbl0569.65081
  15. [15] H. WERNER and R. SCHABACK, Praktische Mathematik II, Springer Berlin-Heidelberg-New York 1979. Zbl0383.65001MR520918
  16. [16] G. N. YAKOVLEV, Boundary properties of functions of class W p ( l ) on regions with angular points, Doklady Academy of Sciences of U.S.S.R. 140, 73-76 (1961). Zbl0112.33204MR136988

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