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Solving the linear elasticity and Stokes equations by an optimal domaindecomposition method derived algebraically involves the use of non standardinterface conditions. The one-level domain decomposition preconditioners arebased on the solution of local problems. This has the undesired consequencethat the results are not scalable, it means that the number of iterationsneeded to reach convergence increases with the number of subdomains. This isthe reason why in this work we introduce, and test numerically, two-levelpreconditioners. 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 hybriddiscontinuous Galerkin and Taylor-Hood discretisations.

Numerical assessment of two-level domain decomposition preconditioners for incompressible Stokes and elasticity equations