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Analysis of an SDG method for the incompressible Navier-Stokes equations. (English) Zbl 1394.76065

Summary: In this paper, we analyze a staggered discontinuous Galerkin (SDG) method for the incompressible Navier-Stokes equations. The method is based on a novel splitting of the nonlinear convection term and results in a skew-symmetric discretization of it. As a result, the SDG discretization has a better conservation property and numerical stability property. The aim of this paper is to develop a mathematical theory for this method. In particular, we will show that the SDG method is well-posed and has an optimal rate of convergence. A superconvergence result will also be shown.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
35Q30 Navier-Stokes equations
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
76D07 Stokes and related (Oseen, etc.) flows
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