MA587: Numerical PDE: Finite Element Method, Sring 2012

Instructor: Dr. Zhilin Li Time: T TH : 4:30pm-5:45pm, SAS 1220
Office: SAS 3148, Tel: 515-3210
Office hours: MW: 10:00-11:00am, TH: 3:00-4:00pm, or by appointment
E-mail: <click to e-mail >

The Finite Element Method is one of very important numerical methods for solving partial differential equations in science and engineering. In this introductory course, we will start with theoretical foundations and algorithm implementations for one-dimensional problems so that we can learn the essential tools that carry over to higher dimensions. The discussion of two-dimensional problems, some common used finite element spaces, error analysis, and other related topics including some applications of the finite element method will then be followed. Efforts will also be made on the issues of implementation and related software packages. Using the data from the Matlab mesh generation, the students will be able to implement finite element method using their favorite computer languages.

Prerequisites:

A reasonable background in calculus, linear algebra, numerical analysis, and partial differential equations.

Grading:

Homework (analytic part and computer projects) about every two weeks: 60%
One mid-term test: 35%, date to be announced
Class participation: 5% (excessive absences will affect the grade linearly)

Text:

Draft of the text book from the instructor plus some references.
C. Johnson, Numerical solution of partial differential equations by the finite element method (optional). Reserved in the D. H. Hill library.

Materials:

FEM for 1D elliptic problems
Introduction
Weak form, minimization problems, and equivalencies
Basis functions
Assembly
Theoretical basis, Sobolev space, Error analysis
Sturm-Liouvillle problem
High order elements
High order equation
Finite element code and data structure
FEM for 2D elliptic problems
Weak form and boundary conditions
Some finite element space
Interpolation and error estimates
FEM programming
Matlab tool-box
FEM for parabolic equation and hyperbolic equations
Applications of FEM

Course Homepage:

http://www4.ncsu.edu/~zhilin/TEACHING/MA587/

A few selected references:

Understanding and Implementing the Finite Element Method by Mark S. Gockenbach, SIAM, 2006.
Finite Element, I-V, G. F. Carey and J. T. Oden, Prentice-Hall, Inc, Englewood Cliffs, 1983.
Partial Differential Equation: (Matlab) Toolbox, The Math-Works Inc.
An Analysis of the Finite Element Method, Second Edition by Gilbert Strang and George Fix, Wellesley-Cambridge Press

Calendar

         January               February                 March  
      
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa 
                                 1  2  3  4                1  2  3
    9 10 11 12 13 14    5  6  7  8  9 10 11    4  B  R  E  A  K 10
15  H 17 18 19 20 21   12 13 14 15 16 17 18   11 12 13 14 15 16 17
22 23 24 25 26 27 28   19 20 21 22 23 24 25   18 19 20 21 22 23 24
29 30 31               26 27 28 29            25 26 27 28 29 30 31

        April                   May                   
       
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa    
 1  2  3  4  H  H  7          1  2  3  4  5                   
 8  9 10 11 12 13 14    6  7  8  9 10 11 12    
15 16 17 18 19 20 21    
22 23 24 25 26  L 28   
29 30

H: Holiday; F: Final Exam; L: Last day of instruction;

Disability services:

Reasonable accommodations will be made for students with verifiable disabilities. In order to take advantage of available accomodations, students must register with Disability Services for Students at 1900 Student Health Center, Campus Box 7509, 515-7653. For more information on NC State's policy on working with students with disabilities, please see the Academic Accommodations for Students with Disabilities Regulation (REG02.20.1)