Domain decomposition algorithms for mortar discretizations

Mortar discretizations have been developed for coupling different approximations in different subdomains, that can arise from engineering applications in complicated structures with highly non-uniform materials. The complexity of the mortar discretizations requires fast algorithms for solving the resulting linear systems. Several domain decomposition algorithms, that have been successfully applied to conforming finite element discretizations, have been extended to the linear systems of mortar discretizations. They are overlapping Schwarz methods, FETI-DP (Dual-Primal Finite Element Tearing and Interconnecting) methods, and BDDC (Balancing Domain Decomposition by Constraints) methods. The new result is that complete analysis, providing the optimal condition number estimate, has been done for geometrically non-conforming subdomain partitions and for problems with discontinuous coefficients. These algorithms were further applied to the twodimensional Stokes and three-dimensional elasticity. In addition, a BDDC algorithm with an inexact coarse problem was developed.