@article{GrajewskiKoesterTurek2009,
  author    = {Grajewski, Matthias and K{\"o}ster, Michael and Turek, Stefan},
  title     = {Mathematical and Numerical Analysis of a Robust and Efficient Grid Deformation Method in the Finite Element Context},
  series = {SIAM Journal on Scientific Computing},
  volume    = {31},
  journal   = {SIAM Journal on Scientific Computing},
  number    = {2},
  publisher = {Society for Industrial and Applied Mathematics},
  address   = {Philadelphia, Pa.},
  doi       = {10.1137/050639387},
  pages     = {1539 -- 1557},
  year      = {2009},
  language  = {en}
}
@article{GrajewskiKoesterTurek2010,
  author    = {Grajewski, Matthias and K{\"o}ster, Michael and Turek, Stefam},
  title     = {Numerical analysis and implementational aspects of a new multilevel grid deformation method},
  series = {Applied Numerical Mathematics},
  volume    = {60},
  journal   = {Applied Numerical Mathematics},
  number    = {8},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0168-9274},
  doi       = {10.1016/j.apnum.2010.03.017},
  pages     = {767 -- 781},
  year      = {2010},
  abstract  = {Recently, we introduced and mathematically analysed a new method for grid deformation (Grajewski et al., 2009) [15] we call basic deformation method (BDM) here. It generalises the method proposed by Liao et al. (Bochev et al., 1996; Cai et al., 2004; Liao and Anderson, 1992) [4], [6], [20]. In this article, we employ the BDM as core of a new multilevel deformation method (MDM) which leads to vast improvements regarding robustness, accuracy and speed. We achieve this by splitting up the deformation process in a sequence of easier subproblems and by exploiting grid hierarchy. Being of optimal asymptotic complexity, we experience speed-ups up to a factor of 15 in our test cases compared to the BDM. This gives our MDM the potential for tackling large grids and time-dependent problems, where possibly the grid must be dynamically deformed once per time step according to the user's needs. Moreover, we elaborate on implementational aspects, in particular efficient grid searching, which is a key ingredient of the BDM.},
  language  = {en}
}