Shock capturing techniques for hp-adaptive finite elements

Alba Hierro, Santiago Badia, Pavel Kus

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)


The aim of this work is to propose an hp-adaptive algorithm for discontinuous Galerkin methods that is capable to detect the discontinuities and sharp layers and avoid the spurious oscillation of the solution around them. In order to control the spurious oscillations, artificial viscosity is used with the particularity that it is only applied around the layers where the solution changes abruptly. To do so, a novel troubled-cell detector has been developed in order to mark the elements around those layers and to impose linear order in them. The detector takes advantage of the evolution of the value of the gradient through the adaptive process.

Original languageEnglish
Pages (from-to)532-553
Number of pages22
JournalComputer Methods in Applied Mechanics and Engineering
Publication statusPublished - 1 Sept 2016
Externally publishedYes


  • Convection-dominated flows
  • Convection–diffusion
  • Discontinuous Galerkin
  • hp-adaptivity
  • Shock capturing
  • Troubled-cell detector

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