Continuous interior penalty finite element method for the time-dependent Navier-Stokes equations: space discretization and convergence

Erik Burman (1) , Miguel Angel Fernández (2)

1 Department of Mathematics [Sussex]
2 REO - Numerical simulation of biological flows

This paper focuses on the numerical analysis of a finite element method with stabilization for the unsteady incompressible Navier-Stokes equations. Incompressibility and convective effects are both stabilized adding an interior penalty term giving L^2-control of the jump of the gradient of the approximate solution over the internal faces. Using continuous equal-order finite elements for both velocities and pressures, in a space semi-discretized formulation, we prove convergence of the approximate solution. The error estimates hold irrespective of the Reynolds number, and hence also for the incompressible Euler equations, provided the exact solution is smooth.

Domaines: Analyse numérique [math.NA]

Erik Burman, Miguel Angel Fernández. Continuous interior penalty finite element method for the time-dependent Navier-Stokes equations: space discretization and convergence. Numerische Mathematik, 2007, 107 (1), pp.39-77. ⟨10.1007/s00211-007-0070-5⟩. ⟨hal-00715243⟩