ERROR-BOUNDS FOR NUMERICAL-SOLUTIONS TO HYDRODYNAMICAL PROBLEMS INVOLVING SHOCKS

Models C and D are mathematical formulations for the motion of materials. Model C is the classical, continuum model and Model D is an alternative with some advantages: Model D has been proved globally well posed; a discretization of Model D has been proved convergent. This paper proves error bounds for the distance between the discrete approximations and the exact solutions to Model D. This is done here for the case when the material law is the ideal gas with a Navier-Stokes viscosity. The boundary data are given by the zero-velocity boundary conditions; the initial data are only required to be physically acceptable. This numerical scheme can be used in the calculation of solutions to problems involving shockwaves in hydrodynamical materials.