Delve into the theoretical framework of finite element analysis $($FEA$)$ as a powerful tool in structural engineering. Explore the fundamental concepts of discretization, element types, and numerical solution techniques employed in FEA. Discuss the advantages and limitations of FEA in modeling complex structural systems, including its ability to capture non$-$linear behavior, dynamic effects, and material heterogeneity. How do engineers validate FEA results against analytical solutions and experimental data to ensure the reliability and accuracy of their structural analyses?