HDG-NEFEM for two dimensional linear elasticity

Abstract

This paper proposes a new methodology for the solution of two dimensional linear elastic problems in domains with curved boundaries. The proposed method exploits the advantages of the hybridisable discontinuous Galerkin method to obtain an accurate approximation of both the displacement and the stress fields by solving a global problem that only involves the displacement field on the element edges as unknown. In addition, the methodology incorporates the exact boundary representation of the domain by means of the so-called NURBS-enhanced finite element method. Numerical examples are used to illustrate the three main advantages of the proposed method, namely the reproducibility of polynomials in domains with curved boundaries, the super-convergence of the solution even for linear approximation and the effectiveness and reliability of degree adaptive processes driven by displacement or stresses.