A super penalty C⁰ discontinuous Galerkin method for Kirchhoff plates

Abstract

A super penalty C 0 discontinuous Galerkin (SPCDG) method is developed for solving the Kirchhoff plate bending problem. For this method, optimal order error estimates in certain broken energy norm and H 1 -norm are established with k 5 where k is the order of the finite element polynomial. Moreover, we analyze the error estimates of the SPCDG method with 1 k <5.

Morley-Wang-Xu element methods with penalty for a fourth order elliptic singular perturbation problem

“…And the C 0 IPDG method was reanalyzed for a layer-adapted mesh in [25]. As a matter of fact, any other discontinuous Galerkin methods for the fourth order elliptic problem [23,53,31,34,32,35,1,33,5,37,42,7,26] can be used to design robust discretizations for problem (1.1).…”