The sharpness of Kuznetsov’s 𝑂(√Δ𝑥)𝐿¹-error estimate for monotone difference schemes

Tang, Tao; Teng, Zhen Huan

doi:10.1090/S0025-5718-1995-1270625-9

The sharpness of Kuznetsov’s $O(\sqrt {\Delta x})\ L^ 1$-error estimate for monotone difference schemes
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by Tao Tang and Zhen Huan Teng PDF

Math. Comp. 64 (1995), 581-589 Request permission

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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