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Numerical methods for multi-dimensional systems of conservation laws. Lecture 1

Wednesday, July 15, 2009 - 9:00am - 10:15am
EE/CS 3-180
Chi-Wang Shu (Brown University)
In this course we will give an introduction to conservative
short capturing numerical methods for solving multi-dimensional
systems of conservation laws. High order accurate finite
difference, finite volume and discontinuous Galerkin finite
element methods will be covered. We will start with the
basic algorithm issues in a simple scalar one dimensional
setting and then describe the generalization to multi-dimensional
systems. A comparison among these different numerical methods
will be provided.

Lecture References:


[1] C.-W. Shu,
Essentially non-oscillatory and weighted essentially
non-oscillatory schemes
for hyperbolic conservation laws
,
in Advanced Numerical
Approximation of Nonlinear Hyperbolic Equations
, B. Cockburn,
C. Johnson,
C.-W. Shu and E. Tadmor (Editor: A. Quarteroni),
Lecture Notes in Mathematics, volume 1697,
Springer, Berlin, 1998, pp.325-432.

[2] C.-W. Shu,
Discontinuous Galerkin methods: general approach and
stability
,
Numerical Solutions of Partial Differential Equations,
S. Bertoluzza, S. Falletta, G. Russo and C.-W. Shu,
Advanced Courses in Mathematics CRM Barcelona,
Birkhäuser, Basel, 2009, pp.149-201.



MSC Code: 
35L65