Abstract
We consider an adaptive C0 Interior Penalty Discontinuous Galerkin (C0IPDG) approximation of the fourth order von Kármán equations with homogeneous Dirichlet boundary conditions and an equilibrated a posteriori error estimator. The C0IPDG method can be derived from a six-field formulation of the finite element discretized von Kármán equations. The equilibrated a posteriori error estimator provides an upper bound for the discretization error in the broken W02,2 norm in terms of the associated primal and dual energy functionals. It requires the construction of equilibrated fluxes and equilibrated moment tensors which can be computed on local patches around interior nodal points of the triangulations. The relationship with a residual-type a posteriori error estimator is studied as well. Numerical results illustrate the performance of the suggested approach.
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