MA692B, Fall 2004
Approximations of Navier-Stokes Equations: numerical analysis
Instructor: Jie Shen
TTh 1:30-2:45PM at REC 123
|Office: MATH 806
Office Hours: TTh 3:00-4:00pm
or by appointment
- Basic existence and uniqueness theory for the Stokes and Navier-Stokes
- Approximations of time dependent Navier-Stokes equations: coupled methods,
penalty methods, artificial compressibility methods, projection
- Implementation with spectral-Galerkin methods;
- Numerical approximations for some other related nonlinear PDEs.
MA611 and CS514. The courses CS614 and CS615 would be
helpful but not necessary.
There will be no exam. Grades will be based on course participation,
homework assignments and programming projects.
Some useful papers
- Roger Temam, Navier-Stokes equations.
Theory and numerical analysis. Reprint of the 1984 edition.
AMS Chelsea Publishing, Providence, RI, 2001. xiv+408 pp. ISBN 0-8218-2737-5.
- Roger Temam, Navier-Stokes equations and nonlinear functional analysis. CBMS-NSF regional conference series in applied mathematics, 66, 1995.
- V. Girault and P.A. Raviart, Finite element methods for
Navier-Stokes equations: theory and algorithms, Springer-Verlag, 1986.
A Navier-Stokes solver by spectral-projection method
A finite diffrence Poisson solver