Finite Element Methods (FEM) revolutionize engineering and scientific computations by breaking down complex systems into smaller elements. Each element represents a discrete region of the domain, facilitating the approximation of solutions through interpolation functions. FEM's adaptability to irregular geometries ensures accuracy while maintaining computational efficiency, making it invaluable for simulating real-world scenarios across disciplines from structural analysis to fluid dynamics. FEM's versatility allows for the incorporation of diverse material properties and boundary conditions, enabling simulations under various conditions. Its widespread adoption in industry and academia underscores its effectiveness in solving challenging engineering problems and providing insights into complex systems. As computational resources advance, FEM's scope and capability are set to further transform numerical simulations and design optimization approaches.