A comparison of mortar and Nitsche techniques for linear elasticity

Domain decomposition techniques provide powerful tools for the numerical approximation of partial differential equations. In this paper, we analyze the Nitsche method for the Lamé operator, establish a priori error estimates and compare this method with the mortar method using dual Lagrange multiplier spaces. Both methods can be applied to non-matching triangulations. We use a multigrid algorithm to solve the algebraic systems. Although we have a mesh dependent bilinear form, optimal W-cycle convergence rates can be obtained. Numerical results for the two methods with linear and quadratic finite elements illustrate the performance and flexibility of these nonconforming discretization techniques.