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Analysis of expanded mixed methods for fourth-order elliptic problems. (English) Zbl 0882.65097

This paper extends to fourth-order elliptic problems some results obtained by the author for numerical solution of second-order elliptic problems. This study differs from the classical ones since three unknowns are simultaneously approximated, i.e., the displacement, the stress tensor and the moment tensor.

Two families of mixed finite elements are analyzed in detail: the Herrmann-Miyoshi and the Herrmann-Johnson families in the context of fourth-order elliptic problems with constant and variable coefficients. The results include abstract error estimates, explicit a priori error estimates of quasi-optimal or optimal order, implementation techniques and numerical examples which prove the efficiency of these methods.

MSC:
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
74K20Plates (solid mechanics)
35J40Higher order elliptic equations, boundary value problems
65N15Error bounds (BVP of PDE)