NE 591 619 Intro to Finite Element Methods
3 Credit Hours
Introduction of the finite element method as a numerical technique for solving linear partial differential equations, using heat conduction, elastostatics and dynamics, and advective/diffusive transport as example systems. Emphasis is placed on the formulation and programming of finite element models, as well as utilization of advanced, open-source software MOOSE to implement them.
Prerequisite
a working knowledge of ordinary and partial differential equations, numerical methods, and programming in MATLAB.
Course Objectives
After completing this course, students will be able to:
- Derive integral forms and variational formulations of partial differential equations.
- Develop finite element approximations for one-dimensional and multidimensional problems.
- Design and implement finite element codes in MATLAB.
- Perform error and stability analyses.
- Solve general partial differential equations using the MOOSE framework.
Course Requirements
| Homework and Programming Assignments | 30% |
| Take-home Midterm | 30% |
| In-class Problems | 10% |
| Take-home Final | 30% |
Course Outline
- Introduction, overview
- Integral forms & Variational Methods
- One-dimensional BVPs
- Multidimensional Problems
- Element design and programming concepts
- Transient Analysis
- Error analysis
- Constrained media problems
- Advective/difusive systems
- Introduction of the MOOSE framework
Textbooks
T.J.R.Hughes, The Finite Element Method (Prentice Hall, 1987)
Software Requirements
The program MATLAB and MOOSE will be used for programming and analysis in this course.
Created: 10/16/2024