Chapter 1: Basics on Finite Elements
ABSTRACT. This lecture notes covers the construction of finite element spaces, focusing on simplicial triangulations. Examples of finite elements, such as the linear Lagrange element, Crouzeix-Raviart element, and higher-order Lagrange elements, are presented. The unisolvence property and continuity of these elements are discussed.
CONTENTS
- An Example: The Linear Finite Element Space
- Simplicial Triangulations
- Finite Element Triple
- More Examples on Finite Elements
- Lagrange Elements
Chapter 1: Basics on Finite Elements
Exercise 5.1. Prove the unisolvence of DoFs and that the Lagrange element function space is globally continuous.
Exercise 5.2. Prove the unisolvence of the three-dimensional Lagrange element and prove that the function space defined is globally continuous.
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