Balancing domain decomposition for mortar mixed finite element methods

The balancing domain decomposition method for mixed finite elements by Cowsar, Mandel, and Wheeler is extended to the case of mortar mixed finite elements on non-matching multiblock grids. The algorithm involves an iterative solution of a mortar interface problem with one local Dirichlet solve and one local Neumann solve per subdomain on each iteration. A coarse solve is used to guarantee that the Neumann problems are consistent and to provide global exchange of information across subdomains. Quasi-optimal condition number bounds are derived, which are independent of the jump in coefficients between subdomains. Numerical experiments confirm the theoretical results.