An Eulerian finite element method for the linearized Navier--Stokes problem in an evolving domain

Abstract

The paper addresses an error analysis of an Eulerian finite element method used for solving a linearized Navier--Stokes problem in a time-dependent domain. In this study, the domain's evolution is assumed to be known and independent of the solution to the problem at hand. The numerical method employed in the study combines a standard Backward Differentiation Formula (BDF)-type time-stepping procedure with a geometrically unfitted finite element discretization technique. Additionally, Nitsche's method is utilized to enforce the boundary conditions. The paper presents a convergence estimate for several velocity--pressure elements that are inf-sup stable. The estimate demonstrates optimal order convergence in the energy norm for the velocity component and a scaled $L^2(H^1)$-type norm for the pressure component.

References in corpus (4)

• On Bogovski\uı and regularized Poincaré integral operators for de Rham complexes on Lipschitz domains
• A CutFEM method for two-phase flow problems
• An unfitted Eulerian finite element method for the time-dependent Stokes problem on moving domains
• A quasi-Lagrangian finite element method for the Navier-Stokes equations in a time-dependent domain

Cited by in corpus (3)

• Stability of instantaneous pressures in an Eulerian finite element method for moving boundary flow problems
• A conservative Eulerian finite element method for transport and diffusion in moving domains
• Geometry Error Analysis of a parametric mapping for Higher Order Unfitted Space-Time Methods