Summation-by-Parts and Correction Procedure via Reconstruction

  • Hendrik RanochaEmail author
  • Philipp Öffner
  • Thomas Sonar
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 119)


The correction procedure via reconstruction (CPR, also known as flux reconstruction), is a framework of high order methods for conservation laws, unifying some discontinuous Galerkin, spectral difference and spectral volume methods. These methods are embedded in the framework of summation-by-parts (SBP) operators with simultaneous approximation terms (SATs), recovering the linearly stable methods of Vincent et al. (J Comput Phys 230(22): 8134–8154, 2011; J Sci Comput 47(1):50–72, 2011; Comput Methods Appl Mech Eng 296:248–272, 2015). The introduction of new correction terms enables stability for Burgers’ equation using nodal bases not including boundary nodes, i.e. Gauss nodes. Extended notions of SBP operators and split-forms are used to obtain stability.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Hendrik Ranocha
    • 1
    Email author
  • Philipp Öffner
    • 1
  • Thomas Sonar
    • 1
  1. 1.Institute Computational MathematicsTU BraunschweigBraunschweigGermany

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