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@ARTICLE{Kremling:903291,
      author       = {Kremling, Gitte and Speck, Robert},
      title        = {{C}onvergence of multilevel spectral deferred corrections},
      journal      = {Communications in applied mathematics and computational
                      science},
      volume       = {16},
      number       = {2},
      issn         = {1559-3940},
      address      = {Berkeley, Calif.},
      publisher    = {Mathematical Sciences Publishers},
      reportid     = {FZJ-2021-04987},
      pages        = {227 - 265},
      year         = {2021},
      abstract     = {The spectral deferred correction (SDC) method is a class of
                      iterative solvers for ordinary differential equations
                      (ODEs). It can be interpreted as a preconditioned Picard
                      iteration for the collocation problem. The convergence of
                      this method is well known, for suitable problems it gains
                      one order per iteration up to the order of the quadrature
                      method of the collocation problem provided. This appealing
                      feature enables an easy creation of flexible, high-order
                      accurate methods for ODEs. A variation of SDC are multilevel
                      spectral deferred corrections (MLSDC). Here, iterations are
                      performed on a hierarchy of levels and an FAS correction
                      term, as in nonlinear multigrid methods, couples solutions
                      on different levels. While there are several numerical
                      examples which show its capabilities and efficiency, a
                      theoretical convergence proof is still missing. We address
                      this issue. A proof of the convergence of MLSDC, including
                      the determination of the convergence rate in the time-step
                      size, will be given and the results of the theoretical
                      analysis will be numerically demonstrated. It turns out that
                      there are restrictions for the advantages of this method
                      over SDC regarding the convergence rate.},
      cin          = {JSC},
      ddc          = {510},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {5111 - Domain-Specific Simulation Data Life Cycle Labs
                      (SDLs) and Research Groups (POF4-511) / DFG project
                      450829162 - Raum-Zeit-parallele Simulation multimodale
                      Energiesystemen (450829162)},
      pid          = {G:(DE-HGF)POF4-5111 / G:(GEPRIS)450829162},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000752484200003},
      doi          = {10.2140/camcos.2021.16.227},
      url          = {https://juser.fz-juelich.de/record/903291},
}