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Two nonconforming finite elements constructed by double set parameter method are used to approximate a fourth order variational inequality with two-sided displacement obstacle. Because the exact solution does not belong to \(H^{4}_{\mathrm{loc}}(\Omega)\) and each element space involves two sets of parameters, a series of novel approaches different from the exiting literature are developed in the procedure for presenting convergence analysis and deriving the optimal error estimates in broken energy norm.

Nonconforming double set parameter finite element methods for a fourth order variational inequality with two-sided displacement obstacle