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The sharpness of Kuznetsov's $ O(\sqrt{\Delta x})\ L\sp 1$-error estimate for monotone difference schemes


Authors: Tao Tang and Zhen Huan Teng
Journal: Math. Comp. 64 (1995), 581-589
MSC: Primary 65M25; Secondary 65M15
DOI: https://doi.org/10.1090/S0025-5718-1995-1270625-9
MathSciNet review: 1270625
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Abstract: We derive a lower error bound for monotone difference schemes to the solution of the linear advection equation with BV initial data. A rigorous analysis shows that for any monotone difference scheme the lower $ {L^1}$-error bound is $ O(\sqrt {\Delta x} )$, where $ \Delta x$ is the spatial stepsize.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1995-1270625-9
Keywords: Monotone difference scheme, error estimate, lower error bound
Article copyright: © Copyright 1995 American Mathematical Society