Summary
A modified variational formulation, recently introduced by Taylor, Beresford and Wilson for solving second order problems, using the nonconforming Wilson element is here analysed. It is shown that the Patch Test is satisfied and that stresses and displacements are respectively first and second order accurate for arbitrary quadrilateral meshes.
Similar content being viewed by others
References
Bramble, J.H., Hilbert, S.H.: Bounds for a class of linear functionals with applications to Hermite interpolation. Numer. Math.16, 362–369 (1971)
Ciarlet, P.G.: The finite element method for elliptic problems. Amsterdam: North Holland, 1978
Ciarlet, P.G., Raviart, P.A.: The combined effect of curved boundaries and numerical integration in isoparametric finite element methods. In: The mathematical foundations of the finite element method with applications to partial differential equations. Aziz, A.K. (ed.). New York: Academic Press, pp. 409–474, 1972
Irons, B.M., Razzaque, A.: Experience with the patch test for convergence of finite elements. In: The mathematical foundations of the finite element method with applications to partial differential equations, Aziz, A.K. (ed.) New York: Academic Press, pp. 557–588, 1972
Lesaint, P.: On the convergence of Wilson's nonconforming element for solving the elastic problem. Comput. Methods Appl. Mech. Engrg.7, 1–16 (1976)
Lesaint, P., Zlámal, M.: Superconvergence of the gradient of finite element solutions. RAIRO13, 139–166 (1979)
Strang, G., Fix, G.J.: An analysis of the finite element method. Englewood Cliffs: Prentice Hall 1973
Taylor, R.L., Beresford, P.J., Wilson, E.L.: A nonconforming element for stress analysis. Internat. J. Numer. Methods Engrg.10, 1211–1219 (1976)
Zienkiewicz, O.C.: The finite element method in engineering science. London: Mac Graw Hill 1971
Zlámal, M.: Superconvergence and reduced integration in the finite element method. Math. Comp.32, 663–685 (1978)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lesaint, P., Zlámal, M. Convergence of the nonconforming Wilson element for arbitrary quadrilateral meshes. Numer. Math. 36, 33–52 (1980). https://doi.org/10.1007/BF01395987
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01395987