An a priori error analysis for a projection based variational multiscale finite element method for Oseen problems in a time-dependent domain

Abstract

Stability and error estimates for a projection based variational multiscale finite element scheme for Oseen problem in a time-dependent domain are derived in this paper. The use of Geometric Conservation Law (GCL) provides an unconditional stable scheme, whereas a restriction on the time-step needs to be imposed to obtain stability estimates independent of the mesh velocity when GCL is violated. Further, a priori error estimate is derived for the semi-discrete problem obtained with the backward Euler time discretization.