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Approximation of a bending plate problem with a boundary unilateral constraint. (English) Zbl 0581.73022

Considered is a unilateral elliptic boundary value problem of forth order, namely the bending problem for a unilaterally supported elastic plate under transverse forces. Firstly, for the class of forces under consideration, existence and uniqueness of the solution is established. Then, for a discretization of mixed type based on Hellan-Hermann- Johnson’s scheme the author proves O(h) and O(h\(| \ln h|^{1/2})\) error bounds for moments and displacement, respectively.
Reviewer: W.Velte

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74G30 Uniqueness of solutions of equilibrium problems in solid mechanics
74H25 Uniqueness of solutions of dynamical problems in solid mechanics
74K20 Plates
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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References:

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