A Mixed Method for the Biharmonic Problem Based On a System of First-Order Equations
SIAM Journal on Numerical Analysis
Isoparametric C0 interior penalty methods for plate bending problems on smooth domains
Calcolo: a quarterly on numerical analysis and theory of computation
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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.