  An entropy-bounded Discontinuous Galerkin (EBDG) scheme is proposed in which
the solution is regularized by constraining the entropy. The resulting scheme
is able to stabilize the solution in the vicinity of discontinuities and
retains the optimal accuracy for smooth solutions. The properties of the
limiting operator according to the entropy-minimum principle are proofed
analytically, and an optimal CFL-criterion is derived. We provide a rigorous
description for locally imposing entropy constraints to capture multiple
discontinuities. Significant advantages of the EBDG-scheme are the general
applicability to arbitrary high-order elements and its simple implementation
for two- and three-dimensional configurations. Numerical tests confirm the
properties of the scheme, and particular focus is attributed to the robustness
in treating discontinuities on arbitrary meshes.
