Weakly nonoscillatory schemes for scalar conservation laws
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- by Kirill Kopotun, Marian Neamtu and Bojan Popov;
- Math. Comp. 72 (2003), 1747-1767
- DOI: https://doi.org/10.1090/S0025-5718-03-01524-2
- Published electronically: April 29, 2003
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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.References
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Bibliographic 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
- 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 - © Copyright 2003 American Mathematical Society
- 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
- MathSciNet review: 1986803