PAPERS
References for ISC5935
Computational PDE's

• Wolfgang Bangerth, Ralf Hartmann, Guido Kanschat,
  DEAL.II - a general-purpose object-oriented finite element library,
  ACM Transactions on Mathematical Software,
  Volume 33, Number 4, article 24, August 2007.
• Evan Bollig, Natasha Flyer, Gordon Erlebacher,
  Solution to PDEs using radial basis function finite-differences (RBF-FD) on multiple GPUs,
  Journal of Computational Physics,
  Volume 231, Issue 21, pages 7133-7151, 20 August 2012.
• C Ross Ethier, D A Steinman,
  Exact fully 3D Navier-Stokes solutions for benchmarking,
  International Journal for Numerical Methods in Fluids,
  Volume 19, Number 5, March 1994, pages 369-375.
• Natasha Flyer, Grady Wright, Bengt Fornberg,
  Radial Basis Function-generated Finite Differences: A Mesh-free Method for Computational Geosciences,
  Geoscience, Accepted.
• Richard Franke,
  A Critical Comparison of Some Methods for Interpolation of Scattered Data,
  Naval Postgraduate School Technical Report,
  NPS-53-79-003, 1979.
• Richard Franke,
  Scattered Data Interpolation: Tests of Some Methods,
  Mathematics of Computation,
  Volume 38, Number 157, January 1982, pages 181-200.
• Frederic Hecht,
  New development in FreeFem++,
  Journal of Numerical Mathematics,
  Volume 20, Number 3-4, 2012, pages 251-265.
• Volker John,
  Reference values for drag and lift of a two-dimensional time-dependent flow around a cylinder,
  International Journal for Numerical Methods in Fluids,
  Volume 44, 2004, pages 777-788.
• Anders Logg, Kent-Andre Mardal, Garth Wells,
  Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book,
  Lecture Notes in Computational Science and Engineering,
  Springer, 2011,
  ISBN13: 978-3642230981
• The Mathworks,
  Partial Differential Equations Toolbox, User's Guide,
  R2014b
• William Mitchell,
  A collection of 2D elliptic problems for testing adaptive grid refinement algorithms,
  Applied Mathematics and Computation,
  Volume 220, 1 September 2013, pages 350-364.
• William Mitchell, Marjorie McClain,
  A comparison of hp-adaptive strategies for elliptic partial differential equations,
  ACM Transactions on Mathematical Software,
  Volume 41, Number 1, Article 2, October 2014.
• Pedro Morin, Ricardo Nochetto, Kunibert Siebert,
  Data Oscillation and Convergence of Adaptive FEM,
  SIAM Journal on Numerical Analysis,
  Volume 38, Number 2, October 2001, pages 466-488.
• C W Oosterlee, P Wesseling, A Segal, E Brakkee,
  Benchmark solutions for the incompressible Navier-Stokes equations in general coordinates on staggered grids,
  International Journal for Numerical Methods in Fluids,
  Volume 17, 1993, pages 301-321.
• Robert Renka, Ron Brown,
  Algorithm 792: Accuracy Tests of ACM Algorithms for Interpolation of Scattered Data in the Plane,
  ACM Transactions on Mathematical Software,
  Volume 25, Number 1, March 1999, pages 78-94.
• Marie Rognes, Anders Logg,
  Automated goal-oriented error control I: stationary variational problems,
  SIAM Journal on Scientific Computing,
  Volume 35, Number 3, 2013, pages C173-C193.
• Scott Sarra, Edward Kansa,
  Multiquadric radial basis function approximation methods for the numerical solution of partial differential equations,
  Advances in Computational Mechanics,
  Volume 2, 2009.
• Varun Shankar, Grady Wright, Robert Kirby, Aaron Fogelson,
  A Radial Basis Function (RBF)-Finite Difference (FD) method for Diffusion and Reaction-Diffusion Equations on Surfaces,
  arXiv:1404.0812v1 [math.NA] 3 Apr 2014.