, Volume 95, Supplement 1, pp 75–88

On optimal node and polynomial degree distribution in one-dimensional \(hp\)-FEM


DOI: 10.1007/s00607-012-0232-x

Cite this article as:
Chleboun, J. & Solin, P. Computing (2013) 95(Suppl 1): 75. doi:10.1007/s00607-012-0232-x


We are concerned with the task of constructing an optimal higher-order finite element mesh under a constraint on the total number of degrees of freedom. The motivation for this work is to obtain a truly optimal higher-order finite element mesh that can be used to compare the quality of automatic adaptive algorithms. Minimized is the approximation error in a global norm. Optimization variables include the number of elements, positions of nodes, and polynomial degrees of elements. Optimization methods and software that we use are described, and numerical results are presented.


\(hp\)-FEM Optimal mesh Optimal polynomial degree Boundary value problem 

Mathematics Subject Classification (2000)

65K99 65L60 65L10 65L50 

Copyright information

© Springer-Verlag Wien 2012

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Civil EngineeringCzech Technical UniversityPrague 6Czech Republic
  2. 2.Department of Mathematics and StatisticsUniversity of NevadaRenoUSA
  3. 3.Institute of ThermomechanicsPragueCzech Republic

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