A viscosity-independent error estimate of a pressure-stabilized Lagrange-Galerkin scheme for the Oseen problem

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.