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A simple preconditioner for a discontinuous Galerkin method for the Stokes problem. (English) Zbl 1299.76128

Summary: We construct Discontinuous Galerkin approximations of the Stokes problem where the velocity field is \(H(\mathrm{div},\Omega)\)-conforming. This implies that the velocity solution is divergence-free in the whole domain. This property can be exploited to design a simple and effective preconditioner for the final linear system.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
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