High order space–time scheme for scalar hyperbolic conservation laws with reduced numerical domain of dependence

Antonio Baeza, Pep Mulet, Dionisio F. Yáñez and David Zorío

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 247, issue C, 93-109

Abstract: In this paper, a novel space–time combined discretization for scalar hyperbolic conservation laws is presented. The resulting scheme is based on obtaining a direct relationship between high order time derivatives and high order space derivatives, in which no mixed derivatives are involved. As a result, schemes of arbitrarily high order in both space and time can be derived, while in turn having a numerical domain of dependence growing linearly with respect to the order, as opposed to classical high order in space and time discretizations, which usually have a numerical domain of dependence that grows quadratically with respect to the order. Finally, in order to tackle discontinuities, WENO reconstructions with efficient weight design and unconditionally optimal accuracy near critical points are used.

Keywords: WENO; High accuracy approximation; Improved adaption to discontinuities (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:247:y:2026:i:c:p:93-109

DOI: 10.1016/j.matcom.2026.03.010

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