| 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
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