  We develop a discretely entropy-stable line-based discontinuous Galerkin
method for hyperbolic conservation laws based on a flux differencing technique.
By using standard entropy-stable and entropy-conservative numerical flux
functions, this method guarantees that the discrete integral of the entropy is
non-increasing. This nonlinear entropy stability property is important for the
robustness of the method, in particular when applied to problems with
discontinuous solutions or when the mesh is under-resolved. This line-based
method is significantly less computationally expensive than a standard DG
method. Numerical results are shown demonstrating the effectiveness of the
method on a variety of test cases, including Burgers' equation and the Euler
equations, in one, two, and three spatial dimensions.
