The active control of flow around an airfoil through morphing is numerically investigated. The lock-in phenomenon was predicted while using a fixed grid. Galerkin/Least-Squares Finite Element Method was used to simulate incompressible flow over an airfoil with leading edge morphing at a Reynolds number, $Re = 5000$, and angle of attack, $\alpha = 6^{\circ}$. The numerical simulation was carried out using the in-house FORTRAN code. The code was validated with the literature by simulating the flow over an oscillating cylinder. The paperwork implemented a locally oscillating surface on the airfoil with a deformation function. The non-dimensional oscillation frequency was varied in the range of [0.4 - 2.7] and the flow frequencies were analyzed. The primary and secondary frequencies were recorded at each simulation and the lock-in region is specified. The streamlines and vorticity contours are presented at two different excitation frequencies, specifically, $f_{e} = 1.0$ and $f_{e} = 2.5$. The streamlines and vorticity contours showed the formation of the vortices in both cases. The results show great accuracy for the Level-Set Method compared with the literature work that used the Arbitrary Lagrangian-Eulerian method, and the flow frequencies can be predicted accurately.