A posteriori discontinuous Galerkin error estimator for linear elasticity.

Abstract

This paper presents for the first time the derivation of an hp a posteriori error estimator for the symmetric interior penalty discontinuous Galerkin finite element method for linear elastic analysis. Any combination of Neumann and Dirichlet boundary conditions are admissible in the formulation, including applying Neumann and Dirichlet on different components on the same region of the boundary. Therefore, the error estimator is applicable to a variety of physical problems. The error estimator is incorporated into an hp-adaptive finite element solver and verified against smooth and non-smooth problems with closedform analytical solutions, as well as, being demonstrated on a non-smooth problem with complex boundary conditions. The hp-adaptive finite element analyses achieve exponential rates of convergence. The performances of the hp-adaptive scheme are contrasted against uniform and adaptive h refinement. This paper provides a complete framework for adaptivity in the symmetric interior penalty discontinuous Galerkin finite element method for linear elastic analysis.