Superconvergent functional output for time-dependent problems using finite differences on summation-by-parts form

Jens Berg, Jan Nordström

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)

Abstract

Finite difference operators satisfying the summation-by-parts (SBP) rules can be used to obtain high order accurate, energy stable schemes for time-dependent partial differential equations, when the boundary conditions are imposed weakly by the simultaneous approximation term (SAT).In general, an SBP-SAT discretization is accurate of order p + 1 with an internal accuracy of 2 p and a boundary accuracy of p Despite this, it is shown in this paper that any linear functional computed from the time-dependent solution, will be accurate of order 2 p when the boundary terms are imposed in a stable and dual consistent way. The method does not involve the solution of the dual equations, and superconvergent functionals are obtained at no extra computational cost. Four representative model problems are analyzed in terms of convergence and errors, and it is shown in a systematic way how to derive schemes which gives superconvergent functional outputs.

Original languageEnglish
Pages (from-to)6846-6860
Number of pages15
JournalJournal of Computational Physics
Volume231
Issue number20
DOIs
Publication statusPublished - 15 Aug 2012
Externally publishedYes

Keywords

  • Dual consistency
  • High order finite differences
  • Stability
  • Summation-by-parts
  • Superconvergence
  • Time-dependent functional output

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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