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

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the finite element method

The Finite Element Method

A self-study course designed for engineering students

course outline
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
course outline con t
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
course outline con t4
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
course outline con t5
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
course outline con t6
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
course outline con t7
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
course outline con t8
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
course outline con t9
Course outline con’t
  • Lesson 45: Exercises
  • Lesson 46: Commercial Codes