Finite Element Theory

Introduction

This is the intro

Basis functions

Basis functions in 1D:

• Linear line (2 pts)
• Quadratic line (3 pts)
• Cubic line (4 pts)

Basis functions in 2D:

• Bi-linear quadrilateral (4 pts)
• Bi-quadratic quadrilateral (9 pts)
• Bi-cubic quadrilateral (16 pts)

Partial Differential Equations

Example adv-diff equation

$$\frac{\partial u}{\partial t} = \Delta \left( u \right) - \nabla \cdot \left( \vec{c} u \right)$$

Example