Analysis of an exactly mass conserving space-time hybridized discontinuous Galerkin method for the time-dependent Navier--Stokes equations

Abstract

We introduce and analyze a space-time hybridized discontinuous Galerkin method for the evolutionary Navier--Stokes equations. Key features of the numerical scheme include point-wise 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.

References in corpus (8)

• MFEM: a modular finite element methods library
• A hybridizable discontinuous Galerkin method for the Navier--Stokes equations with pointwise divergence-free velocity field
• Analysis of a hybridized/interface stabilized finite element method for the Stokes equations
• An embedded--hybridized discontinuous Galerkin finite element method for the Stokes equations
• An exactly mass conserving space-time embedded-hybridized discontinuous Galerkin method for the Navier-Stokes equations on moving domains
• A locally conservative and energy-stable finite element for the Navier--Stokes problem on time-dependent domains
• Preconditioning of a hybridized discontinuous Galerkin finite element method for the Stokes equations
• Analysis of a space--time hybridizable discontinuous Galerkin method for the advection--diffusion problem on time-dependent domains

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• A Reynolds-semi-robust method with hybrid velocity and pressure for the unsteady incompressible Navier--Stokes equations
• Error estimates for finite element discretizations of the instationary Navier-Stokes equations
• A conforming sliding mesh technique for an embedded-hybridized discontinuous Galerkin discretization for fluid-rigid body interaction