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

DOI:
https://doi.org/10.1090/S0025-5718-03-01524-2

Published electronically:
April 29, 2003

MathSciNet review:
1986803

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Abstract | References | Similar Articles | Additional Information

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

Email:
kopotunk@cc.umanitoba.ca

**Marian Neamtu**

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

Email:
neamtu@math.vanderbilt.edu

**Bojan Popov**

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

Email:
popov@math.tamu.edu

DOI:
https://doi.org/10.1090/S0025-5718-03-01524-2

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