<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Abreu, Eduardo</style></author><author><style face="normal" font="default" size="100%">Arthur Espírito Santo</style></author><author><style face="normal" font="default" size="100%">Lambert, Wanderson</style></author><author><style face="normal" font="default" size="100%">Pérez, John</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Convergence, bounded variation properties and Kruzhkov solution of a fully discrete Lagrangian–Eulerian scheme via weak asymptotic analysis for 1D hyperbolic problems</style></title><secondary-title><style face="normal" font="default" size="100%">Numerical Methods for Partial Differential Equations</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">fully discrete Lagrangian–Eulerian scheme</style></keyword><keyword><style  face="normal" font="default" size="100%">Kruzhkov entropy condition</style></keyword><keyword><style  face="normal" font="default" size="100%">maximum principle</style></keyword><keyword><style  face="normal" font="default" size="100%">no-flow curves</style></keyword><keyword><style  face="normal" font="default" size="100%">positivity-preserving</style></keyword><keyword><style  face="normal" font="default" size="100%">total variation nonincreasing</style></keyword><keyword><style  face="normal" font="default" size="100%">weak asymptotic analysis</style></keyword><keyword><style  face="normal" font="default" size="100%">weak bounded variation</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2023</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://onlinelibrary.wiley.com/doi/abs/10.1002/num.22972</style></url></web-urls></urls><number><style face="normal" font="default" size="100%">3</style></number><volume><style face="normal" font="default" size="100%">39</style></volume><pages><style face="normal" font="default" size="100%">2400-2443</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Abstract We design and implement an effective fully discrete Lagrangian–Eulerian scheme for a class of scalar, local and nonlocal models, and systems of hyperbolic problems in 1D. We propose statements, via a weak asymptotic analysis, which include existence, uniqueness, regularity, and numerical approximations of entropy-weak solutions computed with the scheme for the corresponding nonlinear initial value problem for the local scalar case. We study both convergence and weak bounded variation (BV) properties of the scheme to the entropy solution (for the local and scalar case) in the sense of Kruzhkov. The approach is based on the improved concept of no-flow curves, as introduced by the authors, and we highlight the strengths of the method: (i) the scheme for systems of hyperbolic problems does not require computation of the eigenvalues (exact or approximate) either to the numerical flux function or the weak CFL stability condition (wCFL) and (ii) we prove the properties: positivity-preserving, total variation nonincreasing, and maximum principle subject to the wCFL. We present numerical experiments to evaluate the shock capturing capabilities of the scheme in resolving the main features for hyperbolic problems: shock waves, rarefaction waves, contact discontinuities, positivity-preserving properties, and nonlinear wave formations and interactions.&lt;/p&gt;
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