Finite Element Method

Textbook

• Susanne C. Brenner , L. Ridgway Scott. The mathematical theory of finite element methods. New York, NY: Springer New York, 2008.
• Daniele Boffi, Franco Brezzi, Michel Fortin. Boffi, Daniele, Franco Brezzi, and Michel Fortin. Mixed finite element methods and applications. Vol. 44. Heidelberg: Springer, 2013.
• Vidar Thomée. Galerkin finite element methods for parabolic problems. Vol. 25. Springer Science & Business Media, 2007.
• Christian Clason. “Numerical partial differential equations.” Lecture notes, University of Duisburg-Essen, 2021. link

Slides

• Chapter 0: Introduction
• Chapter 1: Overview of the Finite Element Method
• Chapter 2: Sobolev Spaces
• Chapter 3: Variational Formulation of Elliptic BVPs
• Chapter 4: Finite Element Space
• Chapter 5: Polynomial Interpolation In Sobolev Spaces
• Chapter 6: Mixed Finite Element Methods
• Chapter 7: Galerkin Approach for Time-Dependent Problems

Codes

• Gauss Legendre
• Poisson FEM 1D P1