Analysis of an exactly mass conserving space-time hybridized discontinuous Galerkin method for the time-dependent Navier–Stokes equations
Keegan L. A. Kirk, Tamás Horváth, Sander Rhebergen
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 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.
Topics & Concepts
MathematicsGalerkin methodDiscontinuous Galerkin methodNavier–Stokes equationsMathematical analysisSpace (punctuation)Applied mathematicsFinite element methodPhysicsCompressibilityMechanicsPhilosophyLinguisticsThermodynamicsAdvanced Numerical Methods in Computational MathematicsComputational Fluid Dynamics and AerodynamicsDifferential Equations and Numerical Methods