  The correction procedure via reconstruction (CPR, also known as flux
reconstruction) is a framework of high order semidiscretisations used for the
numerical solution of hyperbolic conservation laws. Using a reformulation of
these schemes relying on summation-by-parts (SBP) operators and simultaneous
approximation terms (SATs), artificial dissipation / spectral viscosity
operators are investigated in this first part of a series. Semidiscrete
stability results for linear advection and Burgers' equation as model problems
are extended to fully discrete stability by an explicit Euler method. As second
part of this series, Glaubitz, Ranocha, \"Offner, and Sonar (Enhancing
stability of correction procedure via reconstruction using summation-by-parts
operators II: Modal filtering, 2016) investigate connections to modal filters
and their application instead of artificial dissipation.
