Residual-based a posteriori error estimate for a mixed Reißner-Mindlin plate finite element method. (English) Zbl 1095.74031

Summary: Reliable and efficient residual-based a posteriori error estimates are established for the stabilised locking-free finite element methods for Reissner-Mindlin plate model. The error is estimated by a computable error estimator from above and below up to multiplicative constants that do depend neither on the mesh-size nor on the plate thickness, and are uniform for a wide range of stabilisation parameter. The error is controlled in norms that are known to converge to zero in a quasi-optimal way. An adaptive algorithm is suggested and run for improving the convergence rates in three numerical examples for thicknesses \(0.1\), \(0.001\) and \(0.001\).


74S05 Finite element methods applied to problems in solid mechanics
74K20 Plates
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
Full Text: DOI


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