Math 809

 

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Syllabus: Click here for details in a PDF file

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Course: Math 809, Numerical Methods for Partial Differential Equations III, MWF 12:30pm @CL109

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Texts: Numerical Methods for Conservation Laws. LeVeque

bulletHandout: MATLAB Overview (MO)
bulletTopics: derivation of conservation laws, weak solutions, viscosity solution, entropy condition, Riemann problem, numerical schemes: Godunov, Lax-Friedrich, Lax-Wendroff, ENO, etc
bulletOffice Hours: MWF 1:30-2:30pm @MW410 and by appointment
bulletGrading: HW(60%),class participation(10%),and final project(30%)
bullet Policy: Late Homework and project will be no credit.
bulletTentative Schedule: updated regularly

 

 

Monday Wednesday Friday
Mar 26

Scalar Hyperbolic Equations:

Linear Advection Equation,

Burger Equation,

Method of Characteristics

 

Mar 28

Numerical Method:

1st Order Upwind

Lax-Wendroff

2nd Upwind

for u_t+ a u_x = 0

 

Mar 30

ENO for u_t + a u_x = 0

Lax-Friedrich Scheme

HW1
Apr 2

Domain of dependence

Weak Solution

Apr 4

Riemann Problem

Shock speed

Apr 6

Entropy Conditions for Discontinuity

HW2
Apr 9

Entropy Condition based on the spreading of characteristics

 

Apr 11

Manipulating Conservation Laws

Entropy Functions

Apr 13

Some Scalar Example:

Traffic Flow

Sound Speed

HW3

Apr 16

Two Phase Flow

Shallow Water Eqns

 

Apr 18

Numerical Method for Linear System Equations

Backward Euler, Lax-Friedrichs, Lax-Wendroff, and Upwind

Apr 20

Local Truncation Error

Stability

The Lax Equivalence Theorem HW4

 


Apr 23

Conservative Methods for Nonlinear Problems

Apr 25

Consistency

Discrete Conservation

 

Apr 27

The Lax-Wendroff Theorem

HW5

 

Apr 30

Godunov's Method

May 2

Discrete entropy condition

May 4

Discrete entropy condition

HW6

May 7

Compactness

Total variation stability

May 9

l_1-contracting numerical methods

Monotone methods

May 11

Higher Order Scheme

HW7

May 14

flux limiter

May 16

slope limiter

May 18

slope limiter for nonlinear eqnation

HW8

May 21

Conference

May 23

Conference

May 25

Conference

May 28

Memorial Day (no class)

May 30

Central Scheme and Spectral Difference

Jun 1

ENO, WENO, Spectral Volume, DG

Jun 4

Final Exams Week

Jun 6

Final Exams Week

Jun 8

Final Exams Week