Finite Element Analysis (FEA) — Lagrange Basis Functions and Numerical Quadrature in 1D Through 3D

In this course, we will discuss the use of Lagrange polynomials in the basis functions in 1D through 3D. The formula for the basis functions is first written in 2D, then in 3D. We will further talk about the Gaussian quadrature for numerical integration. Lastly, triangular and tetrahedral elements are discussed using these basis functions. This course was developed by Prof. Krishna Garikipati and Dr. Gregory Teichert, at the University of Michigan in partnership with Ansys.