A unified formulation for interface coupling and frictional contact modeling with embedded error estimation

We present a derivation of a new interface formulation via a merger of continuous Galerkin and discontinuous Galerkin concepts, enhanced by the variational multiscale method. Developments herein provide treatment for the pure-displacement form and mixed form of small deformation elasticity as applied to the solution of two problem classes: domain decomposition and contact mechanics with friction. The proposed framework seamlessly accommodates merger of different element types within subregions of the computational domain and nonmatching element faces along embedded interfaces. These features are retained in the treatment of multibody small deformation contact problems as well, where an unbiased treatment of the contact interface stands in contrast to classical master/slave constructs. Numerical results for problems in two and three spatial dimensions illustrate the robustness and versatility of the proposed method.