Big Picture

What is the big idea behind the Finite Element Method?

The Finite Element Method is a way to turn a partial differential equation into a collection of algebraic equations.

How is that helpful? Why would I want to trade in one type of equation for another?

Algebraic equations are fundamentally easier to understand and solve.

The theory of directly solving partial differential equations is limited to simple problems with highly symmetric domains and boundary conditions.

However, algebraic equations are well-understood and are easily solved by computers.

Why should I consider finite elements instead of finite differences, finite volumes, etc?

• Generality: FEM applies to many different disciplines
• Geometry: FEM works well with complicated geometries
• Efficiency: FEM produces sparse systems of equations that are easy to solve