  This paper presents the construction of novel stabilized finite element
methods in the convective-diffusive context that exhibit correct-energy
behavior. Classical stabilized formulations can create unwanted artificial
energy. Our contribution corrects this undesired property by employing the
concepts of dynamic as well as orthogonal small-scales within the variational
multiscale framework (VMS). The desire for correct energy indicates that the
large- and small-scales should be $H_0^1$-orthogonal. Using this orthogonality
the VMS method can be converted into the streamline-upwind Petrov-Galerkin
(SUPG) or the Galerkin/least-squares (GLS) method. Incorporating both large-
and small-scales in the energy definition asks for dynamic behavior of the
small-scales. Therefore, the large- and small-scales are treated as separate
equations.
  Two consistent variational formulations which depict correct-energy behavior
are proposed: (i) the Galerkin/least-squares method with dynamic small-scales
(GLSD) and (ii) the dynamic orthogonal formulation (DO). The methods are
presented in combination with an energy-decaying generalized-$\alpha$
time-integrator. Numerical verification shows that dissipation due to the
small-scales in classical stabilized methods can become negative, both on a
local and global scale. The results show that without loss of accuracy the
correct-energy behavior can be recovered by the proposed methods. The
computations employ NURBS-based isogeometric analysis for the spatial
discretization.
