Fundamentals of FEM

The harder version

Chapter 1

Intro to 1 Degree of Freedom Second Order PDE

Appendix 4.I.1

Equivalence of Strong and Weak Forms

Global and Local Coordinates

Method of Weighted Residuals

Chapter 2

Heat Transfer

Elastostatics

FE Pseudocode

Linear Space

Vectors will appear in the problems, so it is important to note that they are distinct from scalars that most people are used to. Rather than a single value, they are list of multiple scalars collected into a single object and reside in a space, $\mathcal{L}$. Vectors obey addition and multiplication rules, though differently traditional scalars.

Vector Addition

$$\begin{align} {\bf u}+{\bf v}&=\left(u_{1}, u_{2}, u_{3}, \ldots u_{n}\right)+\left(v_{1}, v_{2}, v_{3}, \ldots v_{n}\right)\\ &=\left(u_{1}+v_{1}, u_{2}+v_{2}, u_{3}+v_{3}, \ldots u_{n}+v_{n}\right) \end{align}$$

Note that subraction works the same as addition using negative vectors, just like how subtraction of scalars is addition using a negative number.

Vector Multiplcation

Multiplication of a vector by a scalar is communitive, just like two scalars.

Inner Product