Weakly over-penalized discontinuous Galerkin schemes for Reissner-Mindlin plates without the shear variable. (English) Zbl 1401.65128
Summary: This paper introduces a new locking-free formulation that combines the discontinuous Galerkin methods with weakly over-penalized techniques for Reissner-Mindlin plates. We derive optimal a priori error estimates in both the energy norm and \(L^2\) norm for polynomials of degree \(k=2\), and we extend the results concerning the energy norm to higher-order polynomial degrees. Numerical tests confirm our theoretical predictions.
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65N15 | Error bounds for boundary value problems involving PDEs |
| 74S05 | Finite element methods applied to problems in solid mechanics |
Software:
PZReferences:
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