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In this paper, we present an adaptive hybridizable $C^0$ discontinuousGalerkin (HCDG) method for Kirchhoff plates. A reliable and efficient aposteriori error estimator is produced for this HCDG method.Quasi-orthogonality and discrete reliability are established with the help of apostprocessed bending moment and the discrete Helmholtz decomposition. Based onthese, the contraction property between two consecutive loops and complexity ofthe adaptive HCDG method are studied thoroughly. The key points in our analysisare a postprocessed normal-normal continuous bending moment from the HCDGmethod solution and a lifting of jump residuals from inter-element boundariesto element interiors.

Quasi-optimal convergence rate for an adaptive hybridizable C0 discontinuous Galerkin method for Kirchhoff plates