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Discontinuous Galerkin approximations of the Stokes and Navier-Stokes equations. (English) Zbl 1273.76077
Summary: Numerical schemes to compute approximate solutions of the evolutionary Stokes and Navier-Stokes equations are studied. The schemes are discontinuous in time and conforming in space and of arbitrarily high order. Fully-discrete error estimates are derived and dependence of the viscosity constant is carefully tracked. It is shown that the errors are bounded by projection errors of the exact solution which exhibit optimal rates when the solutions are smooth.

MSC:
76D05 Navier-Stokes equations for incompressible viscous fluids
76D07 Stokes and related (Oseen, etc.) flows
76M10 Finite element methods applied to problems in fluid mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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