Convergence analysis of optimization-based domain decomposition methods for a bonded structure

We study two optimization-based domain decomposition methods for a bonded structure: the least squares conjugate gradient method and the Uzawa conjugate gradient method. Using the Steklov–Poincaré operator, we show that both methods solve the same underlying linear equation with a symmetric and coercive operator. The convergence analysis is developed using the properties of the trace operator associated to the coupled problem. Numerical experiments show that the Lagrange multiplier approach is more efficient unless a suitable norm is used in the least squares formulation.