Discontinuous Galerkin Methods for Solids and Structures

Abstract

In this article, we provide an overview of discontinuous Galerkin (DG) methods for the modeling of solid and structures. The key feature of a DG method is the use of spaces of discontinuous basis functions; this enables several desirable features in the area of computational modeling such as high-order accuracy for generally-shaped mesh elements, simplified hp adaptive mesh refinement implementation and ease of computer parallelization. Nevertheless, the Finite Element Method still represents the reference numerical technique in the area of solid and structural modeling. Thus, the main motivation for this work is to present the formulation and application of DG methods to various solid and structures problems, which are of interest in area of computational structural integrity, whilst highlighting the benefits in terms of high-order accuracy and ease of parallelization with conventional and non-conventional meshes.