Abstract
In this note, we prove that Summation-by-parts finite difference schemes approximating linear initial-boundary-value problems are stable in \(L^{\infty }\). This, along with the standard \(L^2\) bound is sufficient for optimal convergence rates.
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Communicated by Jan Hesthaven.
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Svärd, M. A note on \(L^{\infty }\) bounds and convergence rates of summation-by-parts schemes. Bit Numer Math 54, 823–830 (2014). https://doi.org/10.1007/s10543-014-0471-7
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DOI: https://doi.org/10.1007/s10543-014-0471-7