A Reduced Local Discontinuous Galerkin Method for Nearly Incompressible Linear Elasticity

A locking-free discontinuous Galerkin method for linear elasticity in locally nearly incompressible heterogeneous media

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On the Local Discontinuous Galerkin Method for Linear Elasticity

Following Castillo et al. 2000 and Cockburn 2003 , a general framework of constructing discontinuous Galerkin DG methods is developed for solving the linear elasticity problem. The numerical traces are determined in view of a discrete stability identity, leading to a class of stable DG methods. A particular method, called the LDG method for linear elasticity, is studied in depth, which can be v...

The Local Discontinuous Galerkin Method for Linear Incompressible Fluid Flow: a Review

A note on the local discontinuous Galerkin method for linear problems in elasticity

Abstract. In this paper we present a mixed local discontinuous Galerkin formulation for linear elasticity problems in the plane with Dirichlet boundary conditions. The approach follows previous dual-mixed methods and introduces the stress and strain tensors, and the rotation, as auxiliary unknowns. Next, we use suitable lifting operators to eliminate part of the unknowns of the corresponding di...

Nearly Incompressible Linear Elasticity Using Simplicial Meshes

We present two finite element methods for simplicial meshes to approximate the solution of the problem of nearly incompressible elasticity. Although both approaches are based on mixed formulations of linear elastic equations and biorthogonal systems, one of them is nonsymmetric, and the other symmetric. An interesting feature of both approaches is that displacement-based formulations can be obt...