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The sharpness of Kuznetsov’s 𝑂(√Δ𝑥)𝐿¹-error estimate for monotone difference schemes
Tao Tang, Zhen Huan Teng
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Source: Crossref
Published: Jan 1, 1995
DOI: 10.1090/s0025-5718-1995-1270625-9
Open original source ↗Source 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 {L^1} -error bound is O ( Δ x ) O(\sqrt {\Delta x} ) , where Δ x \Delta x is the spatial stepsize.
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