TAM 574 Term Project: Spacetime Discontinuous Galerkin Method for

This project involves implementation in one space dimension and time of spacetime discontinuous Galerkin (SDG) methods for linear elastodynamics. You will investigate two versions: a single-field displacement method and a three-field model with independent interpolations for displacement, velocity and strain. The formulations of the methods are described below. 2 Specific Instructions 1. The example problem involves a uniform elastic rod subjected to shock loading. The rod’s material properties are Young’s modulus E = 1 and ρ = 1, so the elastic wave speed is c = E/ρ = 1. The rod has length L = 1, and the body force is b = 0 in all cases. (a) Smooth loading: The rod is fixed at both ends (u(0, ·) = u(L, ·) = 0) (see Figure 1). The initial displacement and velocity fields are u|t=0 = 0 and u̇|t=0 = 2pic sin(2pix) cos(2pict). For reference, the exact solution is u(x, t) = sin(2pix) sin(2pict)