This course discusses why and how finite element analysis (FEA) works and the special properties of FEA. The norms that represent the finite-dimensional trial solution will be discussed. The important properties of the finite element method consistency and the best approximation will be explained in detail. Later, we will discuss the Pythagorean theorem. The Sobolev estimates and convergence of the FEM will be explained further. Lastly, we will talk about finite element error estimation.
This course was developed by Prof. Krishna Garikipati and Dr. Gregory Teichert, at the University of Michigan in partnership with Ansys.