Entropic regularization of Discontinuous Galerkin method in one-dimensional problems of gas dynamics

A new variational entropic regularization principle is formulated for a discontinuous Galerkin (DG) method. An entropy stable DG method of high accuracy is constructed for 1D equations of gas dynamics. The DG solutions satisfy the discrete analogues of the conservation laws of mass, momentum, total energy and entropic inequality. Formulas for the coefficients of the DG method are obtained.