Numerical Methods for the Optimal Control of Scalar Conservation Laws
  We are interested in a class of numerical schemes for the optimization of nonlinear hyperbolic partial differential equations. We present continuous and discretized relaxation schemes for scalar, one-- conservation laws. We present numerical results on tracking type problems with nonsmooth desired states and convergence results for higher--order spatial and temporal discretization schemes. 
M. Herty, L. Pareschi, S. Steffensen
math.OC math.NA