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A quadratic finite element method for solving biharmonic problems in ℝn

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Summary

A family of simplicial finite element methods having the simplest possible structure, is introduced to solve biharmonic problems in ℝn,n≧3, using the primal variable. The family is inspired in the MORLEY triangle for the two dimensional case, and in some sense this element can be viewed as its member corresponding to the valuen=2.

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References

  1. Adams, R.A.: Sobolev Spaces, New York: Academic Press 1975

    Google Scholar 

  2. Ciarlet, P.G.: The finite element method for elliptic problems. Amsterdam: North Holland 1978

    Google Scholar 

  3. Gallic, S.M.: Système de Stokes stationnaire en dimension 3; Formulation en ψ et formulation enu, p dans le cas axisymétrique. Thèse de Doctorat de 3e cycle, Université Pierre et Marie Curie, Paris, 1982

    Google Scholar 

  4. Ladyzhenskava, O.A., Ural'ceva, N.N.: Linear and Quasilinear Elliptic Equations. New York: Academic Press 1968

    Google Scholar 

  5. Lascaux, P. and Lesaint, P.: Some nonconforming finite elements for the plate bending problem, RAIRO Ser. Rouge, Analyse Numérique R-1, 9–53 (1975)

    Google Scholar 

  6. Morley, L.S.D.: The triangular equilibrium element in the solution of plate bending problems, Aero Quart.19, 149–169 (1968)

    Google Scholar 

  7. Ruas, V.: Some results on the curved plate bending problem solved with nonconforming finite elements. Calcolo.10, 120 (1978)

    Google Scholar 

  8. Ruas, V.: Finite element solution of three-dimensional viscous flow problems using nonstandard degrees of freedom. Japan J. Appl. Math.2, 415–431 (1985)

    Google Scholar 

  9. Ruas, V.: Solution of the 3D Navier-Stokes equations in vector potential formulation, via the constant stress finite element method, submitted to the First Int. Conf. on Comp. Meth. in Flow Analysis, to be held in Okayama, Japan in 1988

  10. Strang, G., Fix, G.: An analysis of the finite element method. Englewood Cliffs: Prentice-Hall 1973

    Google Scholar 

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Authors and Affiliations

  1. Pontificia Universidade Católica, 22453, Rio de Janeiro, Brazil

    Vitoriano Ruas

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  1. Vitoriano Ruas
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Ruas, V. A quadratic finite element method for solving biharmonic problems in ℝn . Numer. Math. 52, 33–43 (1987). https://doi.org/10.1007/BF01401020

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  • DOI: https://doi.org/10.1007/BF01401020

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