Quasi-optimal Convergence Rate for an Adaptive Hybridizable C0 Discontinuous Galerkin Method for Kirchhoff Plates
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In this paper, we present an adaptive hybridizable C0C0 discontinuous Galerkin (HCDG) method for Kirchhoff plates. A reliable and efficient a posteriori error estimator is produced for this HCDG method. Quasi-orthogonality and discrete reliability are established with the help of a postprocessed bending moment and the discrete Helmholtz decomposition. Based on these, the contraction property between two consecutive loops and complexity of the adaptive HCDG method are studied thoroughly. The key points in our analysis are a postprocessed normal–normal continuous bending moment from the HCDG method solution and a lifting of jump residuals from inter-element boundaries to element interiors.
A posteriori error estimates; Adaptive hybridizable C-0 discontinuous Galerkin method; Convergence; Computational complexity; Kirchhoff plate bending problems
Quasi-optimal Convergence Rate for an Adaptive Hybridizable C0 Discontinuous Galerkin Method for Kirchhoff Plates.
Numerische Mathematik, 139(4),