A Genuinely Multidimensional High-Resolution Scheme for the Elastic–Plastic Wave Equation

In this paper we present a numerical method of high order for solving the multidimensional elastic–plastic wave equation. The basic idea is to decompose the hyperbolic PDE into advection equations, which can be solved numerically. Furthermore, the occurrence of plasticity makes it necessary to solve an ODE for the stress–strain relationship at every point.