The use of the discontinuous Galerkin method for solving one-dimensional hyperbolic problems of hyperelasticity in an inhomogeneous medium

The work is devoted to the numerical study of the high-order discontinuous Galerkin method for solving a hyperbolic system of equations of hyperelasticity in an inhomogeneous medium. The physical problems and implementation features of computational algorithms for a system of hyperbolic equations written in conservative and nonconservative forms are considered. Zones of uniformity of medium properties are described using smoothed characteristic functions. The results of numerical calculations in homogeneous and inhomogeneous media (gaseous and solid) in the framework of a single statement are presented.