Citing HermesΒΆ

If you use Hermes for your work, please be so kind to include some of the references below as appropriate.

Monographs:

@Book{Hermes-book1,
   author = {P. Solin, K. Segeth, I. Dolezel},
   title = {Higher-Order Finite Element Methods},
   publisher = {Chapman & Hall / CRC Press},
   year = {2003}
}
@Book{Hermes-book2,
   author = {P. Solin},
   title = {Partial Differential Equations and the Finite Element Method},
   publisher = {J. Wiley & Sons},
   year = {2005}
}

Reference to the Hermes open-source project:

@Manual{Hermes-project,
   title =  {Hermes - Higher-Order Modular Finite Element System (User's Guide)},
   author = {P. Solin et al.},
   url =    {http://hpfem.org/}
}

Underlying algorithms (hanging nodes, adaptivity, shape functions):

@Article{Hermes-time-integration,
  author = {P. Solin, L. Korous},
  title = {Adaptive Higher-Order Finite Element Methods for Transient PDE Problems Based on
  Embedded Higher-Order Implicit Runge-Kutta Methods},
  journal = {J. Comput. Physics},
  year = {2011},
  status = {accepted},
  volume = {},
  pages = {}
}
@Article{Hermes-hanging-nodes,
  author = {P. Solin, J. Cerveny, I. Dolezel},
  title = {Arbitrary-Level Hanging Nodes and Automatic Adaptivity in the hp-FEM},
  journal = {Math. Comput. Simul.},
  year = {2008},
  volume = {77},
  pages = {117 - 132}
}
@Article{Hermes-adaptivity,
  author = {P. Solin, D. Andrs, J. Cerveny, M. Simko},
  title = {PDE-Independent Adaptive hp-FEM Based on Hierarchic Extension of Finite Element Spaces},
  journal = {J. Comput. Appl. Math.},
  year = {2010},
  volume = {233},
  pages = {3086-3094}
}
 @Article{Hermes-shape-functions,
   author = {P. Solin, T. Vejchodsky},
   title = {Higher-Order Finite Elements Based on Generalized Eigenfunctions of the Laplacian},
   journal = {Int. J. Numer. Methods Engrg},
   year = {2007},
   volume = {73},
   pages = {1374 - 1394}
 }

Selected applications:

 @Article{Hermes-polymer-metal-composites,
   author = {D. Pugal, P. Solin, K.J. Kim, A. Aabloo},
   title = {Modeling Ionic Polymer-Metal Composites with Space-Time Adaptive Multimesh hp-FEM},
   journal = {Communications in Computational Physics},
   year = {2011},
   status = {accepted},
   volume = {},
   pages = {}
 }
 @Article{Hermes-anisotropic-benchmarks,
   author = {P. Solin, O. Certik, L. Korous},
   title = {Three Anisotropic Benchmarks for Adaptive Finite Element Methods},
   journal = {Appl. Math. Comput.},
   year = {2011},
   status = {accepted},
   volume = {},
   pages = {}
 }
 @Article{Hermes-richards,
   author = {P. Solin, M. Kuraz},
   title = {Solving the Nonstationary Richards Equation with Adaptive hp-FEM},
   journal = {Advanced Water Resources},
   year = {2011},
   volume = {34},
   pages = {1062-1081}
 }
 @Article{Hermes-nuclear,
   author = {L. Dubcova, P. Solin, G. Hansen, H. Park},
   title = {Comparison of Multimesh hp-FEM to Interpolation and Projection Methods for Spatial Coupling of Reactor Thermal and Neutron Diffusion Calculations},
   journal = {J. Comput. Physics},
   year = {2011},
   volume = {230},
   pages = {1182-1197}
 }
 @Article{Hermes-heat-and-moisture,
   author = {P. Solin, L. Dubcova, J. Kruis},
   title = {Adaptive hp-FEM with Dynamical Meshes for Transient Heat and Moisture Transfer Problems},
   journal = {J. Comput. Appl. Math},
   year = {2010},
   volume = {233},
   pages = {3103-3112}
 }
 @Article{Hermes-thermoelasticity,
   author = {P. Solin, J. Cerveny, L. Dubcova, D. Andrs},
   title = {Monolithic Discretization of Linear Thermoelasticity Problems via Adaptive Multimesh hp-FEM},
   journal = {J. Comput. Appl. Math},
   status = {published online},
   doi = {doi 10.1016/j.cam.2009.08.092},
   year = {2009}
 }
 @Article{Hermes-electromagnetics,
   author = {L. Dubcova, P. Solin, J. Cerveny, P. Kus},
   title = {Space and Time Adaptive Two-Mesh hp-FEM for Transient Microwave Heating Problems},
   journal = {Electromagnetics},
   year = {2010},
   volume = {30},
   pages = {23 - 40}
 }
 @Article{Hermes-fluid-mechanics,
   author = {P. Solin, J. Cerveny, L. Dubcova, I. Dolezel},
   title = {Multi-Mesh hp-FEM for Thermally Conductive Incompressible Flow},
   journal = {Proceedings of ECCOMAS Conference COUPLED PROBLEMS 2007 (M. Papadrakakis, E. Onate,
              B. Schrefler Eds.), CIMNE, Barcelona},
   year = {2007},
   pages = {677 - 680}
 }

Other papers that may be still closer to what you need can be found in the citing section of the hp-FEM group home page.

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