Stable Dynamical Adaptive Mesh Refinement

Tomas Lundquist, Jan Nordström, Arnaud Malan

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


We consider accurate and stable interpolation procedures for numerical simulations utilizing time dependent adaptive meshes. The interpolation of numerical solution values between meshes is considered as a transmission problem with respect to the underlying semi-discretized equations, and a theoretical framework using inner product preserving operators is developed, which allows for both explicit and implicit implementations. The theory is supplemented with numerical experiments demonstrating practical benefits of the new stable framework. For this purpose, new interpolation operators have been designed to be used with multi-block finite difference schemes involving non-collocated, moving interfaces.

Original languageEnglish
Article number43
JournalJournal of Scientific Computing
Issue number3
Publication statusPublished - Mar 2021


  • Accuracy
  • Inner product preserving
  • Interpolation
  • Semi-boundedness
  • Stability
  • Transmission problem

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • General Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics


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