In recent years, energy generation and harvesting took the attention of many researchers, especially the piezoelectric materials for their unique characteristics. One of the promising techniques for energy harvesting is the ocean wave energy harvester resulting from the pressure coming from the ocean movement waves on a vertical cantilever with piezoelectric patches, this results in a fluid-structure interaction. A mathematical model is presented based on the Stokes equation for the flow and the Euler-Bernoulli beam theory for the structure motion. The finite element method (FEM) coupled with the quadratic differential method (QDM) are used to numerically solve the resulting partial differential equations with an implicit time scheme. The obtained numerical simulations are validated and discussed. Results show clear effect of the water pressure on the cantilever, as well as the pulsatile behavior of the water motion. This paper gives an adaptive numerical scheme to solve the FSI model for energy harvesting of ocean wave motion and the study gives more insights on the understanding of such problems.