Error estimates for finite-element Navier-Stokes solvers without standard Inf-Sup conditions

Abstract

The authors establish error estimates for recently developed finite-element methods for incompressible viscous flow in domains with no-slip boundary conditions. The methods arise by discretization of a well-posed extended Navier-Stokes dynamics for which pressure is determined from current velocity and force fields. The methods use C ¹ elements for velocity and C ⁰ elements for pressure. A stability estimate is proved for a related finite-element projection method close to classical time-splitting methods of Orszag, Israeli, DeVille and Karniadakis.

Keywords

Time-dependent incompressible flow / Projection method / Backward facing step / Driven cavity / Stokes pressure / Leray projection / Obtuse corner / Recycling

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