1. The Finite Element Method
A self-study course designed for engineering students

2. Course Outline Lesson 1: Introduction and overview
Lesson 2: Brief history of the FEM
Lesson 3: Basic concepts
Lesson 4: Review of numerical methods
Vectors
Matrices
Lesson 5: Method of Weighted Residuals
Classical Solution Technique
The Weak Statement

3. Course Outline con’t Lesson 6: 1-D Element
Lesson 7: Shapes Functions – 1-D
Lesson 8: Steady State Diffusion Equation
Lesson 9: Natural Coordinate System
Lesson 10: Time-Dependence
Lesson 11: Matrix Formulation
Lesson 12: Solution Methods

4. Course outline con’t Lesson 13: 2-D Triangular Element
Lesson 14: The Mesh - triangles
Lesson 15: Shape Functions
Lesson 16: Area Coordinate System
Lesson 17: Numerical Integration
Lesson 18: Steady-State Diffusion Equation
Lesson 19: Time Dependence

5. Course outline con’t Lesson 20: Bandwidth Lesson 21: Exercises
Lesson 22: 2-D Quadrilateral Element
Lesson 23: The Mesh - quadrilaterals
Lesson 24: Shape Functions
Lesson 25: Natural Coordinate System
Lesson 26: Gaussian Quadrature Integration

6. Course outline con’t Lesson 27: Steady-State Diffusion Equation
Lesson 28: Time Dependence (2)
Lesson 29: Isoperimetric Element
Lesson 30: Natural Coordinate System
Lesson 31: Shape Functions
Lesson 32: Element Matrices
Lesson 33: FEM vs. FDM/FVM

7. Course outline con’t Lesson 34: The Chapeau Function
Lesson 35: Accuracy
Lesson 36: 3-D Elements
Lesson 37: The Mesh (3)
Lesson 38: Shape Functions
Lesson 39: Applications – Elasticity
Lesson 40: Applications – Heat Transfer

8. Course outline con’t Lesson 41: Applications – Fluid Flow
Ideal
Incompressible (penalty vs equal order)
Compressible
Lesson 42: Applications – Environmental
Lesson 43: Mesh Adaptation (h vs p)
Lesson 44: Boundary Elements

9. Course outline con’t
Lesson 45: Exercises
Lesson 46: Commercial Codes