A C0 Interior Penalty Discontinuous Galerkin Method and an equilibrated a posteriori error estimator for a nonlinear fourth order elliptic boundary value problem of p-biharmonic type

Abstract

We consider a C0 Interior Penalty Discontinuous Galerkin (C0IPDG) approximation of a nonlinear fourth order elliptic boundary value problem of p-biharmonic type and an equilibrated a posteriori error estimator. The C0IPDG method can be derived from a discretization of the corresponding minimization problem involving a suitably defined reconstruction operator. The equilibrated a posteriori error estimator provides an upper bound for the discretization error in the broken W2,p norm in terms of the associated primal and dual energy functionals. It requires the construction of an equilibrated flux and an equilibrated moment tensor based on a three-field formulation of the C0IPDG approximation. The relationship with a residual-type a posteriori error estimator is studied as well. Numerical results illustrate the performance of the suggested approach.