The Finite Element Method

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