Space-time least-squares spectral elements for convection-dominated unsteady flows

Legendre polynomials are employed in a space-time least-squares spectral element formulation applied to linear and nonlinear hyperbolic scalar equations. No stabilization techniques are required to render a stable, high-order-accurate scheme. In parts of the domain where the underlying exact solution is smooth, the scheme exhibits exponential convergence with polynomial enrichment, whereas in parts of the domain where the underlying exact solution contains discontinuities the solution displays a Gibbs-like behavior. Numerical results will be given in which the capabilities of the space-time formulation to capture discontinuities will be demonstrated.