Monolithic convex limiting in discontinuous Galerkin discretizations of hyperbolic conservation laws

In this work we present a framework for enforcing discrete maximum principles in discontinuous Galerkin (DG) discretizations. The developed schemes are applicable to scalar conservation laws as well hyperbolic systems. Our methodology limiting volume terms is similar recently proposed methods continuous approximations, while DG flux require novel stabilization techniques. Piecewise Bernstein polynomials employed shape functions the spaces, thus facilitating use of very high order spatial approximations. We discuss design new, provably invariant domain preserving scheme that then extended by state-of-the-art subcell limiters obtain high-order bound approximation. procedures can be formulated semi-discrete setting. Thus convergence steady state solutions not inhibited algorithm. numerical results variety benchmark problems. Conservation considered study linear and nonlinear problems, Euler equations gas dynamics shallow water system.