Jan Glaubitz, Jan Nordstrom, Philipp Offner

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


Summation-by-parts (SBP) operators are popular building blocks for systematically developing stable and high-order accurate numerical methods for time-dependent differential equations. The main idea behind existing SBP operators is that the solution is assumed to be well approximated by polynomials up to a certain degree, and the SBP operator should therefore be exact for them. However, polynomials might not provide the best approximation for some problems, and other approximation spaces may be more appropriate. In this paper, a theory for SBP operators based on general function spaces is developed. We demonstrate that most of the established results for polynomial-based SBP operators carry over to this general class of SBP operators. Our findings imply that the concept of SBP operators can be applied to a significantly larger class of methods than is currently known. We exemplify the general theory by considering trigonometric, exponential, and radial basis functions.

Original languageEnglish
Pages (from-to)733-754
Number of pages22
JournalSIAM Journal on Numerical Analysis
Issue number2
Publication statusPublished - 2023


  • exponential functions
  • general function spaces
  • mimetic discretization
  • radial basis functions
  • summation-by-parts operators
  • trigonometric functions

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics


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