A Mixed Method for the Biharmonic Problem Based On a System of First-Order Equations
SIAM Journal on Numerical Analysis
Computers & Mathematics with Applications
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We deal with the Kirchhoff--Love model for a bending thin plate with physical boundary conditions. We propose here a new mixed formulation, based on a decomposition of the bending moment. For its discretization, we employ classical low-order conforming finite elements. Then the discrete formulation allows us to obtain directly an approximation of the bending moment, while the deflection is recovered by solving an additional second order elliptic problem. We establish optimal error estimates which prove that the method is unconditionally convergent. Moreover, its convergence rate is optimal whenever the exact solution is sufficiently smooth.