  We provide a method to compute the entropy-satisfying weak solution to the
eikonal equation in an arbitrary-order polynomial space. The method uses an
artificial viscosity approach and is demonstrated for the signed distance
function, where exact solutions are available. The method is designed
specifically for an existing high-order discontinuous-Galerkin framework, which
uses standard convection, diffusion, and source terms. We show design order of
accuracy and good behavior for both shocks and rarefaction type solutions.
Finally the distance function around a complex multi-element airfoil is
computed using a high-order-accurate representation.
