Interpolation with Discontinuous Functions: Application to Calculation of Shocks
by W. L. Miranker, A. Morreeuw
An interpolation procedure, which uses a step function plus a polynomial correction, is devised and studied for application to the numerical solution of problems having discontinuous solutions. We apply the interpolation procedure to the calculation of shock waves produced by a single convex conservation law. The resulting algorithm does not have the usual undesirable numerical features associated with shock-wave calculations. The stability and convergence of the algorithm is also demonstrated.