# Error Estimates for Semi-discrete Gauge Methods for
the Navier-Stokes Equations : First-Order Schemes

Ricardo H. Nochetto

Department of Mathematics

University of Maryland, College Park

College Park, MD 20742, USA

rhn@math.umd.edu
Jae-Hong Pyo

Department of Mathematics

Purdue University

West Lafayette IN 47907, USA.

pjh@math.purdue.edu
##
Abstract

The gauge formulation of the Navier-Stokes equations for incompressible
fluids is a new projection method.
It splits the velocity $\u=\a+\na\phi$ in terms of auxiliary
(non-physical) variables $\a$ and $\phi$, and replaces the momentum
equation by a heat-like equation for $\a$ and the incompressibility
constraint by a diffusion equation for $\phi$.
This paper studies four time-discrete algorithms based on this
splitting and the backward Euler method for $\a$ with explicit
boundary conditions, and shows their stability and
rates of convergence
for both velocity and pressure. The analyses are variational and hinge
on realistic regularity requirements on the exact solution and data.
Both Neumann and
Dirichlet boundary conditions are, in principle, admissible for $\phi$
but a compatibility restriction for the latter is uncovered which
limits its applicability.