@Article{DominguesGomeRousSchn:2008:AdMuSc,
               author = "Domingues, Margarte Oliveira and Gomes, Sonia M. and Roussel, 
                         Olivier and Schneider, Kai",
          affiliation = "{Instituto Nacional de Pesquisas Espaciais (INPE)} and 
                         {Universidade Estadual de Campinas (UNICAMP)} and {Institut 
                         f{\"u}r Technische Chemie und Polymerchemie (TCP)} and 
                         {Laboratoire de Mod{\'e}lisation et Simulation Num{\'e}rique en 
                         M{\'e}canique et G{\'e}nie des Proc{\'e}d{\'e}s (MSNM-GP)}",
                title = "An adaptive multiresolution scheme with local time stepping for 
                         evolutionary PDEs",
              journal = "Journal of Computational Physics",
                 year = "2008",
               volume = "227",
               number = "8",
                pages = "3758--3780",
                month = "Apr.",
             keywords = "finite volume, adaptivity, multiresolution, evolutionary partial 
                         differential equation.",
             abstract = "We present a fully adaptive numerical scheme for evolutionary PDEs 
                         in Cartesian geometry based on a second-order finite volume 
                         discretization. A multiresolution strategy allows local grid 
                         refinement while controlling the approximation error in space. For 
                         time discretization we use an explicit Runge-Kutta scheme of 
                         second-order with a scale-dependent time step. On the finest scale 
                         the size of the time step is imposed by the stability condition of 
                         the explicit scheme. On larger scales, the time step can be 
                         increased without violating the stability requirement of the 
                         explicit scheme. The implementation uses a dynamic tree data 
                         structure. Numerical validations for test problems in one space 
                         dimension demonstrate the efficiency and accuracy of the local 
                         time-stepping scheme with respect to both multiresolution scheme 
                         with global time stepping and finite volume scheme on a regular 
                         grid. Fully adaptive three-dimensional computations for 
                         reaction-diffusion equations illustrate the additional speed-up of 
                         the local time stepping for a thermo-diffusive flame 
                         instability.",
                  doi = "10.1016/j.jcp.2007.11.046",
                  url = "http://dx.doi.org/10.1016/j.jcp.2007.11.046",
                 issn = "0021-9991",
             language = "en",
           targetfile = "an adaptive.pdf",
        urlaccessdate = "06 maio 2024"
}