Norms — Lesson 1

In this lesson we will cover:

  • Understanding why FEA works and the special properties of FEA.
  • Understanding how FEA convergence works; the mathematical proof will be provided.

Norms that represent the finite-dimensional trial solution, also called the finite element solution, will be introduced in this lesson, as well as the Lagrange polynomial basic function.

In this lesson, we continue with the definition of norms. The Hilbert and Sobolev norms will be introduced, as well as the energy norm. In addition, the inner product notification and bilinear form notification will be covered.

Answering Frequently Asked Questions

In this video we will answer the following questions:
Is the equivalence of norms a fundamental property based on the definition of the particular norms?
Can it be proven mathematically?