A new discontinuous Galerkin method for Kirchhoff plates

A Superconvergent $$C^0$$ C 0 Discontinuous Galerkin Method for Kirchhoff Plates: Error Estimates, Hybridization and Postprocessing

“…Very recently, some CDG methods with minimal penalization were developed, e.g. the CDG method in [37] and the reduced LCDG method in [35]. With the help of Zienkiewicz-Guzmán-Neilan element space designed in [29], we also constructed a reliable and efficient a posteriori error estimator for the reduced LCDG method in [35].…”

“…Through introducing lifting operators, Wells and Dung proposed in [45] a C 0 DG (CDG) method whose penalty coefficients can be precisely quantified a priori. Following the ideas in [9,11], we presented a general framework of constructing CDG methods in [32] and achieved a class of unconditionally stable CDG methods for Kirchhoff plate bending problems. Moreover, as a special case, we designed and analyzed a local CDG (LCDG) method in the previous paper, which is easier to implement than the CDG method in [45].…”

“…Following the ideas in [32] but with the normal bending moment and twisting moment as new numerical traces, we first propose a modified framework of CDG methods for Kirchhoff plates. By choosing numerical traces in a technical way, we derive a superconvergent C 0 discontinuous Galerkin method for Kirchhoff plates.…”

“…the CDG method in [37] and the reduced LCDG method in [35]. With the help of Zienkiewicz-Guzmán-Neilan element space designed in [29], we also constructed a reliable and efficient a posteriori error estimator for the reduced LCDG method in [35]. Through canceling the term of global lifting operator and enhancing the term related to local lifting operators, a compact CDG method possessing the compact stencil was proposed in [1], where only the degrees of freedom belonging to neighboring elements were connected.…”

“…The other point is that both the HHJ method and the mixed method in [5] have made use of the technique of hybridization to reduce the globally coupled degrees of freedom, only leave behind unknowns related to the Lagrange multiplier function and the approximate deflection function u h , which decreases the size of the resulting linear system greatly. Now, let us discuss our CDG method in [32] which is also built upon the Hermann-Miyoshi formulation, with the variables σ and u approximated by piecewise polynomials of degrees l and k, respectively. We can find from [34] (cf.…”