Finite Element Analysis (FEA) and Computational Fluid Dynamics (CFD) are numerical methods used to simulate physical phenomena; however, they address different types of problems.

FEA is commonly used for structural analysis—determining the response of a structure under load. Moreover, it can study deformation, stress distribution, and other attributes related to solid mechanics. Consequently, it is primarily applied in fields like civil, mechanical, and aerospace engineering.

On the other hand, CFD is employed for analyzing fluid flow problems. For instance, this can involve simulating the flow of air over a plane wing or water through a pipe. Additionally, CFD is widely used in aerospace, automotive, HVAC, and environmental engineering.

The mathematical approach differs significantly as well. FEA solves equations related to stress-strain or heat transfer, whereas CFD solves the Navier-Stokes equations that govern fluid flow. Therefore, the two methods cater to distinct sets of problems.

Furthermore, FEA handles phenomena like plastic deformation and fractures in materials, while CFD manages turbulence, heat transfer, and chemical reactions in fluid flows.

For complex problems involving interaction between solid and fluid domains—known as Fluid-Structure Interaction (FSI)—both FEA and CFD may be used in a coupled manner. In summary, the choice between FEA and CFD depends largely on the specific problem and the physical phenomena to be simulated.