  We consider a pressure-stabilized Lagrange-Galerkin scheme for the transient
Oseen problem with small viscosity. In the scheme we use the equal-order
approximation of order $k$ for both the velocity and pressure, and add a
symmetric pressure stabilization term. We show an error estimate for the
velocity with a constant independent of the viscosity if the exact solution is
sufficiently smooth. Numerical examples show high accuracy of the scheme for
problems with small viscosity.
