University of Pennsylvania
School of Engineering and Applied Science
Department of Mechanical Engineering and Applied Mechanics



Please do not print this material on the SEAS or CETS printers.
MEAM 527
Finite Element Analysis
Spring 2000/ S. Turteltaub

Press the reload button for latest version

Table of Contents


Announcements

Handouts

General Information

Course Description

 

Homework

Exam

Links

 



 
 

Announcements

(return to top)
 
 


Course description and syllabus

This is an introductory course for finite element methods used for elliptic and parabolic problems. Typical applications are equilibrium and diffusion problems such as elasticity, heat and mass transfer, potential flow, diffusion of chemical species, etc. Topics covered include: classical and variational formulations, Ritz and Galerkin methods for one and two-dimensional elliptic problems, finite element discretization, direct and iterative methods (Cholesky, gradient and conjugate gradient methods), application to optimization of continuous systems, finite element formulation for parabolic systems, time-integration schemes, stability analysis.
 
 

(return to top)


Prerequisites


Students planning on taking this course are expected to be familiar with partial differential equations, linear algebra and elementary calculus. Programming experience is useful.

(return to top)
 
 


Course Meeting Time

Tuesdays and Thursdays, 4:30 - 6:00 PM. Towne 309.
 
 

(return to top)


Grading Policy

(return to top)

Online Schedule

Week
 Topics covered
 Notes
  1 [1/18-20] Review of PDEs. Strong and weak formulations for one-dimensional boundary value problems  
  2 [1/25-27] Galerkin method. Finite element method with piecewise linear functions.   
 3 [2/1-3] Finite element methods for the two-dimensional heat equation.  
 4 [2/8-10] Direct methods for linear systems of equations. Cholesky's method.    
 5 [2/15-17] Element formulation. Assembly of stiffness matrix and load vector. Numerical integration.   
 6 [2/22-24] FEM for linear elasticity.  
 7 [2/29-3/2] General formulation of elliptic problems. Introduction to finite element spaces.   
8 [3/7-9] Examples of discrete spaces and common finite elements. Triangulations. Error estimates  Midterm 1: March 9
 9 Spring break    
10 [3/21-23] Iterative methods for linear systems of equations.   
 11 [3/23-25] Gradient and conjugate gradient methods.  
12 [3/28-30] Finite element methods for parabolic problems. Semi-discrete variational formulation  
13 [4/4-6] Discretization in time: alpha-methods (forward and backward Euler, Crank-Nicolson). Stability analysis.  
14 [4/11-13] Asymptotic behavior; Gear method.  
15 [4/18-20] Special topics  Midterm 2: April 20
16 [4/25-27] Special topics
Final     

(return to top)
 
 


Textbooks

Recommended Textbook: Additional references: A comprehensive database for finite element books can be found at http://ohio.ikp.liu.se/fe/
 
(return to top)



 
 

General Information

Instructor:


Instructor Office Hours:

(return to top)
 



 
 

Handouts


PostScript version
PDF version
Notes on finite element formulation for linear elasticity
PS version
PDF version

(return to top)



 
 

Homework


Homework Assignments and  Due Dates:
 
Homework
Due date
PDF version
1
 
HW1: PDF version
2
 
HW2: PDF version
3
 
HW3: PDF version
4
 
HW4: PDF version
5
 
HW5: PDF version
6
 
HW6: PDF version

 
 
 

(return to top)
 
 





Homework Solutions:

 
Homework
PDF version
1
Solution: HW1: PDF version
2
Solution: HW2: PDF version
3 Solution: HW3: PDF version
4 Solution: HW4: PDF version

 
 
 
 
 
 

(return to top)



 
 

Exams


Exam Dates:

Midterm 1: March 9 -- 4:30 - 6:00 PM (T309)
Midterm 2: April 20 -- 4:30 - 6:00 PM (T309)
 

(return to top)
 
 


Links

CETS

SEAS

University of Pennsylvania Library System
 
 

(return to top)


Created: 1/99
Last Updated: 3/99