Viscous splitting approximation of mixed hyperbolic-parabolic convection-diffusion equations

We first analyse a semi-discrete operator splitting method for nonlinear, p ossibly strongly degenerate, convection-diffusion equations. Due to strong degeneracy, solutions can be discontinuous and are in general not uniquely determined by their data. Hence weak solutions satisfying an entropy condit ion are sought, We then propose and analyse a fully discrete splitting meth od which employs a front tracking scheme for the convection step and a fini te difference scheme for the diffusion step. Numerical examples are present ed which demonstrate that our method can be used to compute physically corr ect solutions to mixed hyperbolic-parabolic convection-diffusion equations.