Weakly nonoscillatory schemes for scalar conservation laws

Authors:
Kirill Kopotun;Marian Neamtu;Bojan Popov
Affiliations:
Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, R3T 2N2, Canada;-;Department of Mathematics, Texas A&M University, College Station, Texas
Venue:
Mathematics of Computation
Year:
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.