Finite element methods (FEM) and finite volume methods (FVM) are distinct numerical techniques used for solving partial differential equations. FEM involves dividing the geometry into meshes and performing piecewise approximations on each mesh, which is ideal for complex geometries. In contrast, FVM focuses on approximating values over the volume surrounding each node, making it particularly effective for conservation laws. While both methods are used in computational fluid dynamics and structural analysis, they have different approaches to discretization and solution techniques. Understanding these differences is crucial for selecting the appropriate method for specific applications.