On the L2 and the H1 couplings for an overlapping domain decomposition method using Lagrange multipliers

In this paper, a comparison of the L2 and the H1 couplings is made for an overlapping domain decomposition method using Lagrange multipliers. The analysis of the local equations arising from the formulation of the coupling of two mechanical models shows that continuous weight functions are required for the L2 coupling term whereas both discontinuous and continuous weight functions can be used for the H1 coupling. The choice of the Lagrange multiplier space is discussed and numerically studied. The paper ends with some numerical examples of an end-loaded cantilever beam and a cracked plate under tension and shear. It is shown that the continuity enforced with the H1 coupling leads to a link with a flexibility that can be beneficial for coupling a very coarse mesh with a very fine one. To limit the effect of the volume coupling on the global response, a narrow coupling zone is recommended. In this case, volume coupling tends to a surface coupling, especially with a L2 coupling. Copyright q 2006 John Wiley & Sons, Ltd.