The Finite Element Method

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The Finite Element Method

• A self-study course designed for engineering
  students

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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

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Course Outline cont

• 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

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Course outline cont

• 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

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Course outline cont

• 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

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Course outline cont

• 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

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Course outline cont

• 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

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Course outline cont

• 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

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Course outline cont

• Lesson 45 Exercises
• Lesson 46 Commercial Codes