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Weakly nonoscillatory schemes for scalar conservation laws

Authors: Kirill Kopotun, Marian Neamtu and Bojan Popov
Journal: Math. Comp. 72 (2003), 1747-1767
MSC (2000): Primary 65M15; Secondary 35L65, 35B05, 35B30
Published electronically: April 29, 2003
MathSciNet review: 1986803
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Abstract: A new class of Godunov-type numerical methods (called here weakly nonoscillatory or WNO) for solving nonlinear scalar conservation laws in one space dimension is introduced. This new class generalizes the classical nonoscillatory schemes. In particular, it contains modified versions of Min-Mod and UNO. Under certain conditions, convergence and error estimates for WNO methods are proved.

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Additional Information

Kirill Kopotun
Affiliation: Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, R3T 2N2 Canada

Marian Neamtu
Affiliation: Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240

Bojan Popov
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77845

Keywords: Scalar conservation laws, Godunov-type schemes, error estimates, weak nonoscillation, relaxed entropic projection
Received by editor(s): March 1, 2001
Received by editor(s) in revised form: January 28, 2002
Published electronically: April 29, 2003
Additional Notes: The first author was supported by NSERC of Canada and by NSF of USA under grant DMS-9705638
The second author was supported by NSF under grant DMS-9803501
The third author was supported by the ONR Grant No. N00014-91-J-1076
Article copyright: © Copyright 2003 American Mathematical Society