# Stability analysis and error estimates of a projection based variational multiscale method for Oseen equations in moving domains

## TL;DR

This paper establishes stability and error estimates for a projection-based variational multiscale method applied to Oseen equations in moving domains, highlighting the role of the Geometric Conservation Law in ensuring unconditional stability.

## Contribution

The paper introduces a stability analysis and first-order error estimates for a variational multiscale method for Oseen equations, emphasizing the impact of GCL on stability.

## Key findings

- Unconditional stability achieved with GCL
- Conditional stability without GCL depends on time step restrictions
- First-order error estimate using backward Euler scheme

## Abstract

Stability and error estimate for the Oseen equations in a projection based variational setup has been derived in this paper. The use of Geometric Conservation Law (GCL) provides unconditional stability whereas without using GCL we have a conditional scheme which imposes restriction on the time step. Further using the stability results derived, we make the first order error estimate using a backward Euler time discretization scheme.