**MA692B, Fall 2004**

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**## Approximations of Navier-Stokes Equations: numerical analysis
and implementation

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****Instructor: **` Jie Shen`

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****TTh 1:30-2:45PM at REC 123 **

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`Office: MATH 806`
`Office Hours: TTh 3:00-4:00pm`
`or by appointment ` |
`Phone: 4-1923`
`Message: 4-1901`
`E-mail: shen@math.purdue.edu` |

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**Topics:**

- Basic existence and uniqueness theory for the Stokes and Navier-Stokes
equations;
- Approximations of time dependent Navier-Stokes equations: coupled methods,
penalty methods, artificial compressibility methods, projection
methods;
- Implementation with spectral-Galerkin methods;
- Numerical approximations for some other related nonlinear PDEs.

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**Prerequisite:**

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MA611 and CS514. The courses CS614 and CS615 would be
helpful but not necessary.
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**Grading Policy:**

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There will be no exam. Grades will be based on course participation,
homework assignments and programming projects.
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**Reference books:**

- 1.
- 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.
- 2.
- Roger Temam, Navier-Stokes equations and nonlinear functional analysis. CBMS-NSF regional conference series in applied mathematics, 66, 1995.
- 3.
- V. Girault and P.A. Raviart, Finite element methods for
Navier-Stokes equations: theory and algorithms, Springer-Verlag, 1986.

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Some useful papers
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A Navier-Stokes solver by spectral-projection method

A finite diffrence Poisson solver