Locking-Free Discontinuous Galerkin Methods in Elasticity
University of Cape Town, South Africa
2017-08-24 ~ 2017-08-24
Science Building No. 1 1418
Discontinuous Galerkin (DG) methods constitute a generalization of the standard conforming finite element method in that they allow for discontinuities in the solution across interior element boundaries. They have various advantages, for example, in representing complex geometries and irregular meshes with hanging nodes, so that they are well suited to adaptive strategies. The purpose of this presentation is to examine conditions under which DG methods are locking-free for nearly-incompressible problems in elasticity. It is shown that while standard DG approaches are indeed locking-free for meshes of triangles or tetrahedra in two and three dimensions respectively, the situation for quadrilaterals (resp. hexahedra) is more complex, and requires modifications of the standard approach to render these stable and convergent. These modifications are discussed and their numerical performance illustrated with various examples.