TY - JOUR

T1 - A pressure-robust discretization of Oseen's equation using stabilization in the vorticity equation

AU - Ahmed, Naveed

AU - Barrenechea, Gabriel R.

AU - Burman, Erik

AU - Guzman, Johnny

AU - Linke, Alexander

AU - Merdon, Christian

PY - 2021/6/14

Y1 - 2021/6/14

N2 - Discretization of Navier-Stokes’ equations using pressure-robust ﬁnite element methods is considered for the high Reynolds number regime. To counter oscillations due to dominating convection we add a stabilization based on a bulk term in the form of a residual-based least squares stabilization of the vorticity equation supplemented by a penalty term on (certain components of) the gradient jump over the elements faces. Since the stabilization is based on the vorticity equation, it is independent of the pressure gradients, which makes it pressure-robust. Thus, we prove pressure-independent error estimates in the linearized case, known as Oseen’s problem. In fact, we prove an O(hk+ 1/2 ) error estimate in the L2-norm that is known to be the best that can be expected for this type of problem. Numerical examples are provided that, in addition to conﬁrming the theoretical results, show that the present method compares favorably to the classical residual-based SUPG stabilization.

AB - Discretization of Navier-Stokes’ equations using pressure-robust ﬁnite element methods is considered for the high Reynolds number regime. To counter oscillations due to dominating convection we add a stabilization based on a bulk term in the form of a residual-based least squares stabilization of the vorticity equation supplemented by a penalty term on (certain components of) the gradient jump over the elements faces. Since the stabilization is based on the vorticity equation, it is independent of the pressure gradients, which makes it pressure-robust. Thus, we prove pressure-independent error estimates in the linearized case, known as Oseen’s problem. In fact, we prove an O(hk+ 1/2 ) error estimate in the L2-norm that is known to be the best that can be expected for this type of problem. Numerical examples are provided that, in addition to conﬁrming the theoretical results, show that the present method compares favorably to the classical residual-based SUPG stabilization.

KW - incompressible Navier–Stokes equations

KW - divergence-free mixed ﬁnite element methods

KW - pressure-robustness

KW - convection stabilization

KW - Galerkin least squares

KW - vorticity equation

UR - https://www.siam.org/publications/journals/siam-journal-on-numerical-analysis-sinum

M3 - Article

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

SN - 0036-1429

ER -