Convergence of time-space adaptive algorithms for nonlinear conservation laws

Authors :: Quang Huy Tran
Marie Postel
Frédéric Coquel
Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP)
Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)
Laboratoire Jacques-Louis Lions (LJLL)
Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)
IFP Energies nouvelles (IFPEN)
École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)
Source :: IMA Journal of Numerical Analysis, IMA Journal of Numerical Analysis, Oxford University Press (OUP), 2012, 32 (4), pp.1440-1483. ⟨10.1093/imanum/drr054⟩, IMA Journal of Numerical Analysis, 2012, 32 (4), pp.1440-1483. ⟨10.1093/imanum/drr054⟩
Publication Year :: 2012
Publisher :: Oxford University Press (OUP), 2012.
Abstract: International audience; A family of explicit adaptive algorithms is designed to solve nonlinear scalar one-dimensional conservation laws. Based on the Godunov scheme on a uniform grid, a first strategy uses the multiresolution analysis of the solution to design an adaptive grid that evolves in time according to the time-dependent local smoothness. The method is furthermore enhanced by a local time-stepping strategy. Both numerical schemes are shown to converge towards the unique entropy solution.