2014
DOI: 10.4208/jcm.1405-m4409
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A Posteriori Error Estimates for Local $C^0$ Discontinuous Galerkin Methods for Kirchhoff Plate Bending Problems

Abstract: We derive some residual-type a posteriori error estimates for the local C 0 discontinuous Galerkin (LCDG) approximations ([31]) of the Kirchhoff bending plate clamped on the boundary. The estimator is both reliable and efficient with respect to the moment-field approximation error in an energy norm. Some numerical experiments are reported to demonstrate theoretical results.Mathematics subject classification: 65N15, 65N30.

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Cited by 4 publications
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“…So far this has not been done in full generality as it comes to the boundary conditions. Most papers deal only with clamped or simply supported boundaries, see [29] for conforming C 1 elements, [9,17,29] for the mixed Ciarlet-Raviart method ( [11]), and [8,7,19,14,21,30,22] for discontinuous Galerkin (dG) methods. The few papers that do address more general boundary conditions, in particular free, are [5,20] in which the nonconforming Morley element is analysed, [3,4] where a new mixed method is introduced and analysed, and [19] where a continuous/discontinuous Galerkin method is considered.…”
mentioning
confidence: 99%
“…So far this has not been done in full generality as it comes to the boundary conditions. Most papers deal only with clamped or simply supported boundaries, see [29] for conforming C 1 elements, [9,17,29] for the mixed Ciarlet-Raviart method ( [11]), and [8,7,19,14,21,30,22] for discontinuous Galerkin (dG) methods. The few papers that do address more general boundary conditions, in particular free, are [5,20] in which the nonconforming Morley element is analysed, [3,4] where a new mixed method is introduced and analysed, and [19] where a continuous/discontinuous Galerkin method is considered.…”
mentioning
confidence: 99%
“…The recovery technique was used to obtain the a posteriori error estimates for the C 0 interior penalty method in [9], the weakly over-penalized symmetric interior penalty method in [10], the interior penalty discontinuous Galerkin (IPDG) method in [30] and the reduced local C 0 discontinuous Galerkin method in [39]. By the ideas in [5], the Helmholtz decomposition was also applied for the a posteriori error analysis for the local C 0 discontinuous Galerkin method in [53] and the C 0 interior penalty method in [33].…”
mentioning
confidence: 99%