The Matrix-vector Equations for Quadratic Basis Functions — Lesson 3

In the last lesson, the element stiffness matrix was derived for a general element. In this lesson, other terms of the matrix-vector version of the finite-dimensional weak form will be found. The discussion starts with a forcing function for a general element, and these concept is extended to the assembly. Global equations for the matrix-vector weak form are written.

 

The video starts with the equations from the previous video. Everything is written in form of matrices, removing the summation. The derivation of the equations for the forcing function continues in this video and the end assembly is performed.

 

In this lesson, some observations and remarks are made for the form derived for quadratic basis functions. These observations and remarks help us to understand the differences that arise due to the use of different basis functions.

 

In this lesson, the discussion is focused upon a Dirichlet-Dirichlet boundary value problem instead of a Dirichlet-Neumann problem. The definition of a nodal solution is discussed at last. With this, the field is defined using the basis function.