Suggested Papers for ISC5939
Finite Element Seminar

• Jochen Alberty, Carsten Carstensen, Stefan Funken,
  Remarks Around 50 Lines of MATLAB: A Short Finite Element Implementation,
  Numerical Algorithms,
  Volume 20, Number 2-3, August 1999, pages 117-137.
• Martin Alnaes, Kent-Andre Mardal,
  On the efficiency of symbolic computations combined with code generation for finite element methods,
  ACM Transactions on Mathematical Software,
  Volume 37, Number 1, Article 6, January 2010.
• Martin Alnaes, Anders Logg, Kristian Olgaard, Marie Rognes, Garth Wells,
  Unified Form Language: a domain-specific language for weak formulations of partial differential equations,
  ACM Transactions on Mathematical Software,
  Volume 40, Number 2, Article 9, February 2014.
• Douglas Arnold, Franco Brezzi, Michel Fortin,
  A stable finite element for the Stokes equations,
  Estratto da Calcolo,
  Volume 21, Number 4, October-December 1984, pages 337-344.
• Ivo Babuska, Werner Rheinboldt,
  Reliable Error Estimations and Mesh Adaptation for the Finite Element Method,
  in International Conference on Computational Methods in Nonlinear Mechanics,
  edited by John Oden,
  Elsevier, 1980,
  ISBN: 0444853820,
  LC: QA808.I57.
• Satish Balay, Shrirang Abhyankar, M Adams, Jed Brown, Peter Brune, Kris Buschelman, Victor Eijkhout, William Gropp, Dinesh Kaushik, Matt Knepley, Lois Curfman McInnes, Karl Rupp, Barry Smith, Hong Zhang,
  The PETSc Users Manual,
  Technical Report ANL-95/11, Revision 3.5.0,
  Argonne National Laboratory, 8 September 2014.
• 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.
• Wolfgang Bangerth, Carsten Burstedde, Timo Heister, Martin Kronbichler,
  Algorithms and data structures for massively parallel generic adaptive finite element codes, ACM Transactions on Mathematical Software,
  Volume 38, Number 2, article 14, December 2011.
• Wolfgang Bangerth, Timo Heister,
  Quo Vadis, Scientific Software?,
  SIAM News,
  Volume 47, Number 1, January/February 2014.
• Marshall Bern,
  Adaptive Mesh Generation,
  in Error Estimation and Adaptive Discretization Methods in Computational Fluid Dynamics Lecture Notes in Computational Science and Engineering,
  edited by Timothy Barth, Herman Deconinck,
  Volume 25, 2003, pages 1-46,
  ISBN: 987-3-642-07841-5.
• Pavel Bochev, Rich Lehoucq,
  On the Finite Element Solution of the Pure Neumann Problem,
  SIAM Review,
  Volume 47, Number 1, March 2005, pages 50-66.
• John Burkardt, Max Gunzburger, Hyung-Chun Lee,
  POD and CVT-based reduced-order modeling of Navier-Stokes flows,
  Computer Methods in Applied Mechanics and Engineering,
  Volume 196, 2006, pages 337-355.
• Chris Cecka, Adrian Lew, E Darve,
  Assembly of Finite Element Methods on Graphics Processors,
  International Journal for Numerical Methods in Engineering,
  Volume 85, Number 5, pages 640-669, 2011.
• Youn-Sha Chan, Albert Fannjiang, Glaucio Paulino, Bao-Feng Feng,
  Finite part integrals and hypersingular kernels,
  Advances in Dynamical Systems,
  Volume 14, Supplement S2, pages 264-269, 2007.
• Francois Cuvelier, Caroline Japhet, Gilles Scarella,
  An efficient way to perform the assembly of finite element matrices in Matlab and Octave,
  INRIA Research Report 8305, May 2013.
• Howard Elman, Alison Ramage, David Silvester,
  Algorithm 866: IFISS, A Matlab Toolbox for Modelling Incompressible Flow,
  ACM Transactions on Mathematical Software,
  Volume 33, Number 2, June 2007, Article 14.
• Richard Falk,
  Error estimates for the approximation of a class of variational inequalities,
  Mathematics of Computation,
  Volume 28, Number 128, October 1974, pages 963-971.
• Jim Fink, Werner Rheinboldt,
  On the Error Behavior of the Reduced Basis Technique for Nonlinear Finite Element Approximations,
  Zeitschrift fuer Angewandte Mathematik und Mechanik,
  Volume 63, 1983, pages 21-28.
• Jouni Freund, Rolf Stenberg,
  On weakly imposed boundary conditions for second order problems,
  Proceedings of the International Conference on Finite Elements in Fluids, New trends and applications,
  Venezia, 15-21 October 1995.
• Isaac Fried,
  Condition of finite element matrices generated from nonuniform meshes,
  AIAA Journal,
  Volume 10, Number 2, 1972, pages 219-221.
• Isaac Fried,
  Bounds on the spectral and maximum norms of the finite element stiffness, flexibility and mass matrices,
  International Journal of Structures and Solids,
  Volume 9, Number 9, September 1973, pages 1013-1034.
• Marcus Garvie, John Burkardt, Jeff Morgan,
  Simple Finite Element Methods for Approximating Predator-Prey Dynamics in Two Dimensions using MATLAB,
  Bulletin of Mathematical Biology,
  Accepted.
• Christophe Geuzaine, Jean-Francois Remacle,
  Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities,
  International Journal for Numerical Methods in Engineering,
  Volume 79, Number 11, pages 1309-1331, 2009.
• William Gordon, Charles Hall,
  Transfinite Element Methods: Blending-Function Interpolation over Arbitrary Curved Element Domains,
  Numerische Mathematik,
  Volume 21, Number 1, February 1973, pages 109-129.
• Max Gunzburger, Janet Peterson,
  On Conforming Finite Element Methods for the Inhomogeneous Stationary Navier-Stokes Equations,
  Numerische Mathematik,
  Volume 42, Number 2, June 1983, pages 173-194.
• Frederic Hecht,
  New development in FreeFem++,
  Journal of Numerical Mathematics,
  Volume 20, Number 3-4, 2012, pages 251-265.
• Michael Heroux, Roscoe Bartlett, Vickie Howle, Robert Hoekstra, Jonathan Hu, Tamara Kolda, Richard Lehoucq, Kevin Long, Roger Pawlowski, Eric Phipps, Andrew Salinger, Heidi Thornquist, Ray Tuminaro, James Willenbring, Alan William, Kendall Stanley,
  An overview of the Trilinos project,
  ACM Transactions on Mathematical Software,
  Volume 31, Number 3, September 2005, pages 397-423.
• Alfa Heryudono, Elisabeth Larsson,
  FEM-RBF: A geometrically flexible, efficient numerical solution technique for partial differential equations with mixed regularity,
  Project FEMRBF Final Report,
  Department of Information Technology, Uppsala University, 2012.
• Claes Johnson, Jukka Saranen,
  Streamline diffusion methods for the incompressible Euler and Navier-Stokes Equations,
  Mathematics of Computation,
  Volume 47, Number 175, pages 1-18, July 1986.
• Matthew Knepley, Andy Terrel,
  Finite Element Integration on GPUs,
  ACM Transactions on Mathematical Software,
  Volume 39, Number 2, Article 10, February 2013.
• Michael Labrosse, Carsten Beller, Munir Boodhwani, Christopher Hudson, Benjamin Sohmer,
  Subject-specific finite element modeling of normal aortic valve biomechanics from 3D+t TEE images,
  Medical Image Analysis,
  Volume 20, 2015, pages 162-172.
• William Layton,
  A two-level discretization method for the Navier-Stokes equations,
  Computers and Mathematics with Applications,
  Volume 26, Number 2, July 1993, pages 33-38.
• William Layton,
  A nonlinear subgrid scale model for incompressible viscous flow problems,
  SIAM Journal on Scientific and Statistical Computing,
  Volume 17, Number 2, March 1996, pages 347-357.
• Xiaoye Li, Meiyu Shao,
  A supernodal approach to incomplete LU factorization with partial pivoting,
  ACM Transactions on Mathematical Software,
  Volume 37, Number 4, Article 43, February 2011.
• Anders Logg, Garth Wells,
  DOLFIN: Automated finite element computing,
  ACM Transactions on Mathematical Software,
  Volume 37, Number 2, Article 20, April 2010.
• Joseph Maubach,
  Local bisection refinement for N-simplicial grids generated by reflection,
  SIAM Journal on Scientific and Statistical Computing,
  Volume 16, Number 1, January 1995, pages 210-227.
• 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.
• Hoa Nguyen, Max Gunzburger, Lili Ju, John Burkardt,
  Adaptive anisotropic meshing for steady convection-dominated problems,
  Computer Methods in Applied Mechanics and Engineering,
  Volume 198, Number 37-40, 2009, pages 2964-2981.
• Kent Olgaard, Garth Wells,
  Optimizations for quadrature representations of finite element tensors through automated code generation,
  ACM Transactions on Mathematical Software,
  Volume 37, Number 1, Article 8, January 2010.
• J Pask, B Klein, P Sterne, C Fong,
  Finite-element methods in electronic-structure theory,
  Computer Physics Communications,
  Volume 135, 2001, pages 1-34.
• J Pask, P Sterne,
  Finite-element methods in ab-initio electronic-structure calculations,
  Modelling and Simulation in Materials Science and Engineering,
  Volume 13, 2005, pages 71-96.
• E Pavarino, L Neves, J Machado, M de Godoy, Y Shiyou, J Momente, G Zafalon, A Pinto, C Valencio,
  Free tools and strategies for the generation of 3D finite element meshes: Modeling of the cardiac structures,
  International Journal of Biomedical Imaging,
  Volume 2013, Article ID 540571, 11 pages.
• Qing Peng, Xu Zhang, Linda Hung, Emily Carter, Gang Lu,
  Quantum simulation of materials at micron scales and beyond,
  Physical Review B,
  Volume 78, 2008, pages 054118-1:054118-14.
• Per-Olof Persson, Gilbert Strang,
  A Simple Mesh Generator in MATLAB,
  SIAM Review,
  Volume 46, Number 2, June 2004, pages 329-345.
• Janet Peterson,
  The Reduced Basis Method for Incompressible Viscous Flows,
  SIAM Journal on Scientific and Statistical Computing,
  Volume 10, Number 4, July 1989, pages 777-786.
• Pradeep Ramuhalli, Lalita Udpa, Satish Udpa,
  Finite-element neural networks for solving differential equations,
  IEEE Transactions on Neural Networks,
  Volume 16, Number 6, November 2005, pages 1381-1392.
• Jason Smart, Andrew McCammon,
  Analysis of synaptic transmission in the neuromuscular junction using a continuum finite element model,
  Biophysical Journal,
  Volume 75, October 1998, pages 1679-1688.
• Martin Stynes,
  Numerical methods for convection-diffusion problems, or The 30 years war,
  arXiv:1306.5172v1 [math.NA] 21 June 2013.
• Jun Takeuchi, Yukio Kosugi,
  Neural network representation of the finite element method,
  Neural Networks,
  Volume 7, Number 2, 1994, pages 389-395.
• Ruediger Verfuerth,
  A posteriori error estimates for finite element discretizations of the heat equation,
  CALCOLO,
  Volume 40, 2003, pages 195-212.
• Lara Vigneron, Romain Boman, Jean-Philippe Ponthot, Pierre Robe, Simon Warfield, Jacques Verly,
  Enhanced FEM-based modeling of brain shift deformation in Image-Guided Neurosurgery,
  Journal of Computational and Applied Mathematics,
  Volume 234, 2010, pages 2046-2053.
• Praveen Yadav, Krishnan Suresh,
  Large Scale Finite Element Analysis via Assembly-Free Deflated Conjugate Gradient,
  Journal of Computing and Information Science in Engineering,
  Volume 14, Number 4, December 2014, 9 pages.