author = "Deiterding, Ralf and Domingues, Margarete Oliveira and Gomes, 
                         S{\^o}nia M. and Schneider, Kai",
          affiliation = "{University of Southampton} and {Instituto Nacional de Pesquisas 
                         Espaciais (INPE)} and {Universidade Estadual de Campinas 
                         (UNICAMP)} and {Universit{\'e} d'Aix-Marseille}",
                title = "Comparison of adaptive multiresolution and adaptive mesh 
                         refinement applied to simulations of the compressible Euler 
              journal = "SIAM Journal on Scientific Computing",
                 year = "2016",
               volume = "38",
               number = "5",
                pages = "S173--S193",
             keywords = "Adaptive numerical methods, Conservation laws, Euler equations, 
                         Local time stepping, Mesh refinement, Multiresolution.",
             abstract = "We present a detailed comparison between two adaptive numerical 
                         approaches to solve partial differential equations, adaptive 
                         multiresolution (MR) and adaptive mesh refinement (AMR). Both 
                         discretizations are based on finite volumes in space with second 
                         order shock-capturing and explicit time integration either with or 
                         without local time stepping. The two methods are benchmarked for 
                         the compressible Euler equations in Cartesian geometry. As test 
                         cases a two-dimensional Riemann problem, Lax-Liu #6, and a 
                         three-dimensional ellipsoidally expanding shock wave have been 
                         chosen. We compare and assess their computational efficiency in 
                         terms of CPU time and memory requirements. We evaluate the 
                         accuracy by comparing the results of the adaptive computations 
                         with those obtained with the corresponding FV scheme using a 
                         regular fine mesh. We find that both approaches yield similar 
                         trends for CPU time compression for increasing number of 
                         refinement levels. MR exhibits more efficient memory compression 
                         than AMR and shows slightly enhanced convergence; however, a 
                         larger absolute overhead is measured for the tested codes.",
                  doi = "10.1137/15M1026043",
                  url = "http://dx.doi.org/10.1137/15M1026043",
                 issn = "1064-8275",
             language = "en",
           targetfile = "ddgs_sisc2016final.pdf",
        urlaccessdate = "24 jan. 2021"