Adaptive reference elements via harmonic extensions and associated inner modes

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A non-intrusive extension to the standard p-version of the finite element method is proposed. Meshes with hanging nodes are handled by adapting the reference elements so that the resulting discretisation is always conforming. The shape functions on these adaptive reference elements are not polynomials, but either harmonic extensions of the boundary restrictions of the standard shape functions or solutions to a local Poisson problem. The numerical experiments are taken from computational function theory and the efficiency of the proposed extension resulting in exponential convergence in the quantities of interest is demonstrated.

Original languageEnglish
Pages (from-to)2272-2288
Number of pages17
JournalComputers and Mathematics with Applications
Issue number11
Publication statusPublished - 1 Dec 2020
MoE publication typeA1 Journal article-refereed


  • Adaptivity
  • Finite element method
  • Harmonic extensions
  • p-version


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