Introduction to Finite Element Methods

TL;DR

This paper provides a comprehensive introduction to finite element methods, covering their mathematical foundations and various approaches for solving elliptic and parabolic partial differential equations.

Contribution

It offers an educational overview of finite element techniques, including conforming, nonconforming, and Galerkin methods, for graduate-level understanding.

Findings

Detailed explanation of finite element theory

Coverage of conforming and nonconforming methods

Introduction to Galerkin methods for parabolic equations

Abstract

These lecture notes for a graduate course present an introduction to the mathematical theory of finite element methods for the numerical solution of partial differential equations. Covered are conforming and nonconforming (in particular, discontinuous Galerkin and mixed methods) for elliptic partial differential equations and Galerkin methods for parabolic equations.