  The paper presents high-order accurate, energy-, and entropy-stable
discretizations constructed from summation-by-parts (SBP) operators. Notably,
the discretizations assemble global SBP operators and use continuous solutions,
unlike previous efforts that use discontinuous SBP discretizations.
Derivative-based dissipation and local-projection stabilization (LPS) are
investigated as options for stabilizing the baseline discretization. These
stabilizations are equal up to a multiplicative constant in one dimension, but
only LPS remains well conditioned for general, multidimensional SBP operators.
Furthermore, LPS is able to take advantage of the additional nodes required by
degree $2p$ diagonal-norms, resulting in an element-local stabilization with a
bounded spectral radius. An entropy-stable version of LPS is easily obtained by
applying the projection on the entropy variables. Numerical experiments with
the linear-advection and Euler equations demonstrate the accuracy, efficiency,
and robustness of the stabilized discretizations, and the continuous approach
compares favorably with the more common discontinuous SBP methods.
