Chapter 5: Finite element discretizations
Abstract
In this book, we primarily focus on the finite element method for spatial discretization of PDEs. This chapter includes a brief coverage of the continuous Galerkin finite element method. In Section 5.1, we discuss finite element discretization of a linear elliptic PDE in two space dimensions. In Section 5.2, we consider the heat equation in a two-dimensional domain and discuss its spatial and temporal discretization. This is done to elucidate the temporal discretization of timedependent PDEs when a finite element approach is used for spatial discretization. To provide some insight regarding numerical solution of nonlinear PDEs, we consider a nonlinear elliptic PDE in Section 5.3.
Fields of Study & Subjects
Advanced Numerical Methods in Computational Mathematics
Matrix Theory and Algorithms
Contact Mechanics and Variational Inequalities
Publication details
- Journal / source
- Society for Industrial and Applied Mathematics eBooks
- Pages
- 61–71
- Publication date
- 27 February 2026
- Language
- EN
- Document type
- Book chapter