DeepAI AI Chat
Log In Sign Up

Inf-sup stabilized Scott-Vogelius pairs on general simplicial grids for Navier-Stokes equations

by   Naveed Ahmed, et al.

This paper considers the discretization of the time-dependent Navier-Stokes equations with the family of inf-sup stabilized Scott-Vogelius pairs recently introduced in [John/Li/Merdon/Rui, arXiv:2206.01242, 2022] for the Stokes problem. Therein, the velocity space is obtained by enriching the H^1-conforming Lagrange element space with some H(div)-conforming Raviart-Thomas functions, such that the divergence constraint is satisfied exactly. In these methods arbitrary shape-regular simplicial grids can be used. In the present paper two alternatives for discretizing the convective terms are considered. One variant leads to a scheme that still only involves volume integrals, and the other variant employs upwinding known from DG schemes. Both variants ensure the conservation of linear momentum and angular momentum in some suitable sense. In addition, a pressure-robust and convection-robust velocity error estimate is derived, i.e., the velocity error bound does not depend on the pressure and the constant in the error bound for the kinetic energy does not blow up for small viscosity. After condensation of the enrichment unknowns and all non-constant pressure unknowns, the method can be reduced to a P_k-P_0-like system for arbitrary velocity polynomial degree k. Numerical studies verify the theoretical findings.


Inf-sup stabilized Scott–Vogelius pairs on general simplicial grids by Raviart–Thomas enrichment

This paper considers the discretization of the Stokes equations with Sco...

Pressure-robust staggered DG methods for the Navier-Stokes equations on general meshes

In this paper, we design and analyze staggered discontinuous Galerkin me...

Unconditional stability and error analysis of an Euler IMEX-SAV scheme for the micropolar Navier-Stokes equations

In this paper, we consider numerical approximations for solving the micr...

Discretizing advection equations with rough velocity fields on non-cartesian grids

We investigate the properties of discretizations of advection equations ...

The pressure-wired Stokes element: a mesh-robust version of the Scott-Vogelius element

The conforming Scott-Vogelius pair for the stationary Stokes equation in...

Two conjectures on the Stokes complex in three dimensions on Freudenthal meshes

In recent years a great deal of attention has been paid to discretizatio...

Improved long time accuracy for projection methods for Navier-Stokes equations using EMAC formulation

We consider a pressure correction temporal discretization for the incomp...