What are the main steps in the finite element method?

The finite element method (FEM) is a powerful numerical technique used to obtain approximate solutions to boundary value problems for partial differential equations. The correct answer emphasizes the key phases of the FEM process, which can be broken down into several important steps.

The first step, discretization, involves dividing a complex domain into simpler, smaller parts called finite elements. This step is crucial because it transforms a continuous problem into a discrete one, allowing for easier mathematical handling and computation.

Next, the formulation of element equations entails establishing mathematical relationships governing the behavior of each individual element. This often involves deriving expressions related to physical laws such as equilibrium, compatibility, and material laws, leading to a system of equations that can be solved.

Following this, the assembly step combines the equations from all individual elements into a global system of equations that represents the entire problem. This step is essential since it integrates the behavior of all elements into one comprehensive model.

Finally, the application of boundary conditions is performed to incorporate the effects of constraints and external influences on the model. Boundary conditions are necessary to ensure that the solution reflects real-world constraints and behaves correctly along the edges or surfaces of the analyzed domain.

These main steps are foundational to effectively employing the finite element method, allowing engineers and researchers to