Coquel, Frédéric; Postel, Marie; Tran, Quang-Huy Convergence of time-space adaptive algorithms for nonlinear conservation laws. (English) Zbl 1273.65119 IMA J. Numer. Anal. 32, No. 4, 1440-1483 (2012). The authors, combining the multiresolution analysis, the finite volume methodology and advanced tools from functional analysis, construct two adaptive explicit finite volume schemes for scalar nonlinear conservation laws. The first scheme uses a global time step and the second one is the local time-stepping strategy. In both cases the convergence in the weak sense of approximate solutions towards the unique entropy solution of the continuous problem is proved. Numerical tests for the Burgers equation with various initial conditions are presented. Reviewer: S. Burys (Kraków) MSC: 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs 65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs 35L65 Hyperbolic conservation laws 35Q53 KdV equations (Korteweg-de Vries equations) Keywords:adaptive algorithms; entropy solution; local time stepping; numerical examples; multiresolution analysis; explicit finite volume schemes; nonlinear conservation laws; convergence; Burgers equation PDF BibTeX XML Cite \textit{F. Coquel} et al., IMA J. Numer. Anal. 32, No. 4, 1440--1483 (2012; Zbl 1273.65119) Full Text: DOI