Accurate solution-adaptive finite difference schemes for coarse and fine grids

Research output: Contribution to journalArticle

Abstract

We introduce solution dependent finite difference stencils whose coefficients adapt to the current numerical solution by minimizing the truncation error in the least squares sense. The resulting scheme has the resolution capacity of dispersion relation preserving difference stencils in under-resolved domains, together with the high order convergence rate of conventional central difference methods in well resolved regions. Numerical experiments reveal that the new stencils outperform their conventional counterparts on all grid resolutions from very coarse to very fine.

Details

Authors
  • Viktor Linders
  • Mark H. Carpenter
  • Jan Nordström
Organisations
External organisations
  • Technion - Israel Institute of Technology
  • NASA Langley Research Center
  • Linköping University
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Computational Mathematics

Keywords

  • Accuracy, Adaptivity, Convergence, Dispersion relation preserving, Finite differences, Least squares
Original languageEnglish
Article number109393
JournalJournal of Computational Physics
Volume410
Publication statusPublished - 2020 Jun
Publication categoryResearch
Peer-reviewedYes