On finite element mesh connection methods for domain decomposition problems

We examine the approximation properties and computational efficiency of three typical mesh connection technologies in the finite element analyses; that is, (1) the penalty method (PM), (2) the discontinuous Galerkin method (DGM) based on the Nitsche's method and (3) the Lagrange multiplier method (LMM) in conjunction with the augmented Lagrangian method (ALM). After formulating the problem and briefly describing the solution methods of these methods, we carry out the series of numerical experiments to compare the performances of PM and DGM, as well as the LMM. Specifically, we examine the effects of the magnitude of penalty parameters in PM and DGM on the accuracy of the approximated displacements or tractions on the interface between the decomposed physical domains, on which the meshes topologies are compatible or incompatible and which, in some cases is identified with the material interface. We are also concerned with the performances and the computational efficiency of interpolation functions of different orders for the Lagrange multipliers in the ALM.