A new finite element formulation for the Kirchhoff plate model is presented. The method is a displacement formulation with the deflection and the rotation vector as unknowns, and it is based on ideas stemming from a stabilized method for the Reissner–Mindlin model [R. Stenberg, in Asymptotic Methods for Elastic Structures, P. Ciarlet, L. Trabucho, and J. M. Viano, eds., de Gruyter, Berlin, 1995] and a method to treat a free boundary [P. Destuynder and T. Nevers, RAIRO Modél. Math. Anal. Numér., 22 (1988), pp. 217–242]. Optimal a priori and a posteriori error estimates are derived.
BEIRAO DA VEIGA, L., Niiranen, J., Stenberg, R. (2007). A family of C0 finite elements for Kirchhoff plates I: error analysis. SIAM JOURNAL ON NUMERICAL ANALYSIS, 45(5), 2047-2071 [10.1137/06067554X].
A family of C0 finite elements for Kirchhoff plates I: error analysis
BEIRAO DA VEIGA, LOURENCOPrimo
;
2007
Abstract
A new finite element formulation for the Kirchhoff plate model is presented. The method is a displacement formulation with the deflection and the rotation vector as unknowns, and it is based on ideas stemming from a stabilized method for the Reissner–Mindlin model [R. Stenberg, in Asymptotic Methods for Elastic Structures, P. Ciarlet, L. Trabucho, and J. M. Viano, eds., de Gruyter, Berlin, 1995] and a method to treat a free boundary [P. Destuynder and T. Nevers, RAIRO Modél. Math. Anal. Numér., 22 (1988), pp. 217–242]. Optimal a priori and a posteriori error estimates are derived.
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