Volume 49, pp. 41-63, 2018.

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

Gabriel R. Barrenechea, Michał Bosy, and Victorita Dolean


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, which 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.

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Key words

Stokes problem, nearly incompressible elasticity, Taylor-Hood, hybrid discontinuous Galerkin methods, domain decomposition, coarse space, optimized restricted additive Schwarz methods.

AMS subject classifications

65F10, 65N22, 65N30, 65N55.

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