Consistency of the Finite Element Method — Lesson 2

In this lesson, we look at an important property of the finite element method, consistency. The consistency condition states that the numerical method should admit the exact solution as one of the solutions that it can find i.e. the exact solution should satisfy the finite-dimensional weak form equation. In this lesson, we mathematically prove this statement. The satisfaction of this condition ensures that the finite element method can recover the exact solution.