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Journal Articles IMA Journal of Numerical Analysis Year : 2012

Convergence of time-space adaptive algorithms for nonlinear conservation laws

Abstract

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.
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Dates and versions

hal-01404120 , version 1 (28-11-2016)

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F. Coquel, M. Postel, Q.-H. Tran. Convergence of time-space adaptive algorithms for nonlinear conservation laws. IMA Journal of Numerical Analysis, 2012, 32 (4), pp.1440 - 1483. ⟨10.1093/imanum/drr054⟩. ⟨hal-01404120⟩
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