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Nonconforming double set parameter finite element methods for a fourth order variational inequality with two-sided displacement obstacle. (English) Zbl 1333.65133

Summary: 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.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
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