New discontinuous Galerkin algorithms and analysis for linear elasticity with symmetric stress tensor

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.

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...

Multigrid algorithms for symmetric discontinuous Galerkin methods on graded meshes

We study a class of symmetric discontinuous Galerkin methods on graded meshes. Optimal order error estimates are derived in both the energy norm and the L2 norm, and we establish the uniform convergence of V -cycle, F -cycle and W -cycle multigrid algorithms for the resulting discrete problems. Numerical results that confirm the theoretical results are also presented.

Discontinuous Galerkin methods for nonlinear elasticity

Discontinuous Galerkin finite element methods for linear elasticity and quasistatic linear viscoelasticity

We consider a finite-element-in-space, and quadrature-in-timediscretization of a compressible linear quasistatic viscoelasticity problem. The spatial discretization uses a discontinous Galerkin finite element method based on polynomials of degree r—termed DG(r)—and the time discretization uses a trapezoidal-rectangle rule approximation to the Volterra (history) integral. Both semiand fully-disc...