A local projection stabilization/continuous Galerkin-Petrov method for incompressible flow problems

A local projection stabilization (LPS) method in space is considered to approximate the evolutionary Oseen equations. Optimal error bounds with constants independent of the viscosity parameter are obtained in the continuous-in-time case for both the velocity and pressure approximation. In addition, the fully discrete case in combination with higher order continuous Galerkin-Petrov (cGP) methods is studied. Error estimates of order k+1 are proved, where k denotes the polynomial degree in time, assuming that the convective term is time-independent. Numerical results show that the predicted order is also achieved in the general case of time-dependent convective terms.