A posteriori discontinuous Galerkin error estimator for linear elasticity

This paper presents for the first time the derivation of a posteriori error estimator for the symmetric interior penalty discontinuous Galerkin finite element method for linear elastic analysis. Pure Neumann/Dirichlet and mixed Neumann/Dirichlet boundary conditions and admissible in the formulation, making the error estimator applicable to variety of physical problems. The error estimator is incorporated into a hp-adaptive finite element solver and verified against smooth and non-smooth problems with closed-form 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 which is the fasted reported so far in literature. The performances of the hp-adaptive scheme are contrasted against uniform and adaptive h refinement. This paper provides complete framework for adaptivity in the symmetric interior penalty discontinuous Galerkin finite element method for linear elastic analysis.