An unconstrained mixed method for the biharmonic problem. (English) Zbl 0982.65124

Very early, R. Glowinski [Topics Numer. Analysis, Proc. Royal Irish Acad. Conf., Dublin 1972, 123-171 (1973; Zbl 0277.35003)] proposed a nonconforming finite element method for the approximation of the clamped biharmonic problem and proved its convergence. By embedding this problem in the framework of the mixed methods following the primal formulation of P. G. Ciarlet and P. A. Raviart [Math. Aspect, Finite Elem. Partial Differ. Equat. Proc. Symp. Madison 1974, 125-145 (1974; Zbl 0337.65058)], the authors extend the analysis to cover the case of smooth boundaries and both simple support and clamped boundary conditions. They also give the respective orders of convergence and some numerical applications which prove the quality of the convergence.
This paper is nicely written and attractive.


65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J40 Boundary value problems for higher-order elliptic equations
74K20 Plates
74S05 Finite element methods applied to problems in solid mechanics
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
Full Text: DOI