MAT 7230, Finite Element Methods

• Instructor: Dr. Zhimin Zhang
  zzhang@math.wayne.edu, http://www.math.wayne.edu/~zzhang, phone: (313)-577-2496 (office), (313)-577-2479 (secretary)
• Course Objective:
  The course is an introduction to the finite element method. It will cover some practical issues such as schemes, implementation, and coding. It will also discuss some limited theoretical aspects. The application of the finite element method to the Poisson equation, heat transfer, and steady state convection-diffusion equations will be discussed. If time permits, finite element methods for solid mechanics including linear elasticity, beam, and plate may also be considered. Special finite element methods such as non-conforming, mixed, p- and hp- version methods will be introduced. The course is designed for graduate students in science, engineering, and mathematics. It is especially suitable for those students who have some previous knowledge of differential equations and numerical methods. For those students who have learned finite element methods in engineering and want to know more about the method and some recent development, this is also a course to consider.
• Prerequisite:
  Potential students should have some basic knowledge of differential equations and linear algebra. Knowledge of one programming language, such as C, C++, Fortran, or Matlab is helpful. Features of object oriented programming in Matlab will be briefly taught in class and sample Matlab programs will be provided.
• Homeworks, Exams and Projects:
  One midterm exam (20%) and one final exam (30%) will be given. Homeworks and computer projects (50%) will be assigned. It is possible for students to focus on the theory part or algorithm part of the course to earn credits. In the former case, midterm and final will be 30% and 40%, respectively, and homework/project 30%. In the latter case, midterm and final will be 10% and 20%, respectively, and homework/project 70%.
• Reference Books:
  1. Dietrich Braess, Finite Elements: Theory, fast solvers, and applications in solid mechanics, Cambridge University Press, New York, 1997. ISBN 0-521-58834-0
  2. Susanne C. Brenner and L. Ridgway Scott: The Mathematical Theory of Finite Element Methods, Springer-Verlag, New York, 1994. ISBN 0-387-94193-2
  3. Claes Johnson, Numerical Solution of Partial Differential Equations by the Finite Element Method, Cambridge University Press, Cambridge, 1987. ISBN 0-521-34758-0
  4. Christoph Schwab, p- and hp-Finite Element Methods: Theory and applications in solid and fluid mechanics, Numerical Mathematics and Scientific Computation. The Clarendon Press, Oxford University Press, New York, 1998. xii+374 pp. ISBN 0-19-850390-3
  5. Barna Szabo and Ivo Babuska: Finite Element Analysis, John-Wiley & Sons, New York, 1991. ISBN 0-471-50273-1