On the Local Discontinuous Galerkin Method for Linear Elasticity
نویسندگان
چکیده
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 viewed as an extension of the LDG method discussed by Castillo et al. 2000 and Cockburn 2003 . The error bounds in L2-norm, H1-norm, and a certain broken energy norm are obtained. Some numerical results are provided to confirm the convergence theory established.
منابع مشابه
Locking-free adaptive discontinuous Galerkin FEM for linear elasticity problems
An adaptive discontinuous Galerkin finite element method for linear elasticity problems is presented. We develop an a posteriori error estimate and prove its robustness with respect to nearly incompressible materials (absence of volume locking). Furthermore, we present some numerical experiments which illustrate the performance of the scheme on adaptively refined meshes.
متن کاملDiscontinuous Galerkin FEM for Elliptic Problems in Polygonal Domains (Abstract)
The present work is concerned with the analysis of the Discontinuous Galerkin Finite Element Method (DGFEM) for linear • diffusion problems, • elasticity problems,
متن کاملDiscontinuous Galerkin and the Crouzeix–raviart Element: Application to Elasticity
We propose a discontinuous Galerkin method for linear elasticity, based on discontinuous piecewise linear approximation of the displacements. We show optimal order a priori error estimates, uniform in the incompressible limit, and thus locking is avoided. The discontinuous Galerkin method is closely related to the non-conforming Crouzeix–Raviart (CR) element, which in fact is obtained when one ...
متن کاملA 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...
متن کاملDiscontinuous Galerkin Methods for Friedrichs' Systems. Part II. Second-order Elliptic PDEs
This paper is the second part of a work attempting to give a unified analysis of Discontinuous Galerkin methods. The setting under scrutiny is that of Friedrichs’ systems endowed with a particular 2×2 structure in which some of the unknowns can be eliminated to yield a system of second-order elliptic-like PDE’s for the remaining unknowns. For such systems, a general Discontinuous Galerkin metho...
متن کامل