On the numerical solution of the first biharmonic equation
M2AN - Modélisation mathématique et analyse numérique, Volume 22 (1988) no. 4, pp. 655-676.
@article{M2AN_1988__22_4_655_0,
     author = {Peisker, P.},
     title = {On the numerical solution of the first biharmonic equation},
     journal = {M2AN - Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {655--676},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {22},
     number = {4},
     year = {1988},
     zbl = {0661.65112},
     mrnumber = {974292},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1988__22_4_655_0/}
}
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Peisker, P. On the numerical solution of the first biharmonic equation. M2AN - Modélisation mathématique et analyse numérique, Volume 22 (1988) no. 4, pp. 655-676. http://www.numdam.org/item/M2AN_1988__22_4_655_0/

[1] O. Axelsson and V. A. Barker, Finite Element Solution of Boundary Value Problems, Theory and Computation. Academic Press 1984. | MR | Zbl

[2] P. E. Bjørstad, Fast numerical solution of the biharmonic Dirichlet problem on rectangles, Siam J. Numer. Anal. 20, 59-71 (1983). | MR | Zbl

[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). | MR | Zbl

[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). | MR | Zbl

[5] P. G. Ciarlet, The Finite Element Method for Elliptic Problems, North Holland 1978. | MR | Zbl

[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). | MR | Zbl

[7] L. W. Ehrlich, Solving the biharmonic equation as a coupled difference equation, Siam J. Numer. Anal. 8, 278-287 (1971). | MR | Zbl

[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). | MR | Zbl

[9] W. Hackbusch, Multi-Grid Methods and Applications, Springer Berlin-Heidelberg-New York, Heidelberg 1985. | Zbl

[10] J. L. Lions, E. Magenes, Non-Homogeneous Boundary Value Problems and Applications I, Springer Berlin-Heidelberg-New York 1972. | Zbl

[11] P. Peisker, Zwei numerische Verfahren zur Lösung der biharmonischen Gleichung unter besonderer Berücksichtigung der Mehrgitteridee, Dissertation, Bochum 1985. | Zbl

[12] J. Pitkäranta, Boundary subspaces for the finite element method with Lagrange multipliers, Numer. Math. 33, 273-289 (1979). | MR | Zbl

[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). | Numdam | MR | Zbl

[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. | Zbl

[15] H. Werner and R. Schaback, Praktische Mathematik II, Springer Berlin-Heidelberg-New York 1979. | MR | Zbl

[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). | MR | Zbl