# Introduction to the Finite Element Method

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 Classical Solution Technique The Weak Statement 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 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 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 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 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 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 Course outline cont Lesson 45: Exercises Lesson 46: Commercial Codes

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