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Applied
Math Seminar
Winter Quarter 2002
3:15 - 4:15 p.m.
Sloan Mathematics Corner
Building 380, Room 380-C
Friday, February 22, 2002
Jan S. Hesthaven
Division of Applied Mathematics
Brown University
High-Order Accurate Unstructured Grid
Methods for Conservation Laws
Abstract:
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The accurate and efficient numerical solution of conservation
laws remains a challengde due to the inherent properties of such problems,
e.g., time-dependence, nonsmooth solutions, nonuniqueness etc. This is
often further complicated by a need to solved problems in complex geometries.
Through a combined use of multivariate polynomial high-order interpolation,
weakly imposed boundary operators and knowlegde about the nature of conservation
laws, robust, high-order accurate and efficient computational methods
for the numerical solution of conservation laws in complex geometries
has recently begun to emerge.
We shall discuss these developments, emphasizing the generality of the
formulation and some of the theoretical results supporting it. The accuracy,
robustness and parallel scalability of the scheme is illustrated through
a number of applications, borrowed from electromagnetics and gasdynamics.
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