Ruijie Liu

Discontinuous Galerkin finite element solution of 3D elasticity

Publisher Summary This chapter presents the way of formulation and implementation of a family of discontinuous Galerkin (DG) finite element methods applied to 3D elastic solids. Discontinuous Galerkin (DG) is an accurate and robust algorithm for modeling elasticity even for almost incompressible materials. Major motivations for applying DG to elasticity problems include a local element-by-element approximation to the momentum equation and average quantities, which can be considered continuous forces or stress fields on an interface. The flexibility of DG methods allows hp refinements with nonconforming adaptive meshes and variable local order of approximation. Because of this local nature of approximation, DG methods only require communication between elements that share faces. Thus, these methods are well suited for parallel computation. Finally, these methods appear to be accurate and robust in terms of treating incompressible materials. Future work needs to address parallel solvers, adaptivity, and geomechanics modeling.