  In this paper, we develop high-order nodal discontinuous Galerkin (DG)
methods for hyperbolic conservation laws that satisfy invariant domain
preserving properties using a subcell flux corrections and convex limiting.
These methods are based on a subcell flux corrected transport (FCT) methodology
that involves blending a high-order target scheme with a robust, low-order
invariant domain preserving method that is obtained using a graph viscosity
technique. The new low-order discretizations are based on sparse stencils which
do not increase with the polynomial degree of the high-order DG method. As a
result, the accuracy of the low-order method does not degrade when used with
high-order target methods. The method is applied to both scalar conservation
laws, for which the discrete maximum principle is naturally enforced, and to
systems of conservation laws such as the Euler equations, for which positivity
of density and a minimum principle for specific entropy are enforced. Numerical
results are presented on a number of benchmark test cases.
