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A stabilized mixed finite element method for the biharmonic equation based on biorthogonal systems. (English) Zbl 1226.65095
The author proposes a stabilized finite element method for the approximation of the biharmonic equation with a clamped boundary condition. The formulation is obtained by introducing the gradient of the solution of the biharmonic equation as a new unknown and writing an additional variational equation in terms of a Lagrange multiplier. An optimal a priori error estimate for the finite element solution when the mesh is uniformly regular is also given.
##### MSC:
 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE) 65N15 Error bounds (BVP of PDE) 65N12 Stability and convergence of numerical methods (BVP of PDE) 35J40 Higher order elliptic equations, boundary value problems 74K20 Plates (solid mechanics) 74S05 Finite element methods in solid mechanics
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