Analysis of an exactly mass conserving space-time hybridized discontinuous Galerkin method for the time-dependent Navier-Stokes equations. (English) Zbl 1504.65206
Summary: We introduce and analyze a space-time hybridized discontinuous Galerkin method for the evolutionary Navier-Stokes equations. Key features of the numerical scheme include pointwise mass conservation, energy stability, and pressure robustness. We prove that there exists a solution to the resulting nonlinear algebraic system in two and three spatial dimensions, and that this solution is unique in two spatial dimensions under a small data assumption. A priori error estimates are derived for the velocity in a mesh-dependent energy norm.
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65M15 | Error bounds 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 |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 35Q30 | Navier-Stokes equations |
Keywords:
Navier-Stokes equations; space-time; hybridized; discontinuous Galerkin; finite element method; error analysisSoftware:
MFEMReferences:
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