The Finite-dimensional Weak Form — Lesson 3

In this lesson, we begin with the infinite-dimensional weak form for linear, elliptic PDEs in three dimensions with scalar variables and derive its equivalent finite-dimensional weak form.

The finite-dimensional weak form is the basis of the finite element formulation. In this lesson, we begin by dividing the problem domain into smaller subdomains called elements and then use these elements to define the underlying finite element basis. Further, we also discuss a general eight-node brick element or hexahedral element and the trilinear basis functions used in its formulation.