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The correction procedure via reconstruction (CPR, also known as fluxreconstruction) is a framework of high order semidiscretisations used for thenumerical solution of hyperbolic conservation laws. Using a reformulation ofthese schemes relying on summation-by-parts (SBP) operators and simultaneousapproximation terms (SATs), artificial dissipation / spectral viscosityoperators are investigated in this first part of a series. Semidiscretestability results for linear advection and Burgers' equation as model problemsare extended to fully discrete stability by an explicit Euler method. As secondpart of this series, Glaubitz, Ranocha, \"Offner, and Sonar (Enhancingstability of correction procedure via reconstruction using summation-by-partsoperators II: Modal filtering, 2016) investigate connections to modal filtersand their application instead of artificial dissipation.

Enhancing stability of correction procedure via reconstruction using summation-by-parts operators I: Artificial dissipation