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Local discontinuous Galerkin methods for the Stokes system. (English) Zbl 1032.65127

A discontinuous Galerkin method for the Stokes problem is introduced and analysed. A priori error estimates for velocity and pressure are derived, which are shown to be optimal, if proper polynomial approximations and stabilization parameters are used. The theoretical mathematical results are confirmed by numerical computations for a simple test case in a square domain. The possibilities for extensions of the results to curvilinear elements and more complex polygonal domains are discussed.
It will be interesting to see results for the extension of the method to the incompressible Navier-Stokes equations, which is announced by the authors for future work.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
76D07 Stokes and related (Oseen, etc.) flows
76M10 Finite element methods applied to problems in fluid mechanics
35Q30 Navier-Stokes equations
65N15 Error bounds for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs

Software:

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