  Solving the linear elasticity and Stokes equations by an optimal domain
decomposition method derived algebraically involves the use of non standard
interface conditions. The one-level domain decomposition preconditioners are
based on the solution of local problems. This has the undesired consequence
that the results are not scalable, it means that the number of iterations
needed to reach convergence increases with the number of subdomains. This is
the reason why in this work we introduce, and test numerically, two-level
preconditioners. Such preconditioners use a coarse space in their construction.
We consider the nearly incompressible elasticity problems and Stokes equations,
and discretise them by using two finite element methods, namely, the hybrid
discontinuous Galerkin and Taylor-Hood discretisations.

Numerical Analysis;Computational Engineering, Finance, and Science;Numerical Analysis