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.
CITATION STYLE
Ranocha, H., Öffner, P., & Sonar, T. (2017). Summation-by-Parts and Correction Procedure via Reconstruction. In Lecture Notes in Computational Science and Engineering (Vol. 119, pp. 627–637). Springer Verlag. https://doi.org/10.1007/978-3-319-65870-4_45
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