Welcome to the class website for Finite Element Methods for Partial Differential Equations. Finite elements provide a class of numerical methods for approximating the solutions of partial differential equations. In this course we will cover both fundamental mathematical concepts and foundations as well as how in practice to develop and apply finite element methods to specific problems. We will develop methods for Elliptic, Parabolic, and Hyperbolic PDEs as well as for non-linear problems.
Please be sure to read the prerequisites and grading policies for the class. Also see the syllabus for more details.
Prerequisites:
A working knowledge of advanced calculus, linear algebra, and partial differential equations will be assumed.
Slides
- Introduction to FEM and Ritz-Galerkin Approximation [PDF] [GoogleSlides]
- Sobolev Spaces [PDF] [GoogleSlides]
- Finite Element Spaces [PDF] [GoogleSlides]
- Finite Element Approximation Properties and Convergence [PDF] [GoogleSlides]
- Variational Formulation of Elliptic PDEs [PDF] [GoogleSlides]
- Elasticity Theory [PDF] [GoogleSlides]
- Finite Element Mixed Methods [PDF] [GoogleSlides]
Supplemental Materials:
- Python General Tutorial
- Python tutorial at Codecademy
- Python 3.7 documentation
- Numpy Python Package Tutorial
- Enthought Canopy integrated analysis environment.
- Jupyter Notebooks: Python Interface
- Example Python Code:
- Neville's Method: [PDF] [Python Code] [Jupyter Notebook]
Class Annoucements:
- A book that you might find helpful for background on Real Analysis is Analysis, by Lieb and Loss [link].
- Supplemental exercises [PDF].