Towards numerical procedures for those technical phenomena whose mathematical models lead to non-standard conservation laws: A survey Original Research Article

An introduction to modelling of physical phenomena by conservation laws will be given, particularly in case of phenomena for which the conservation-law-models do not show the standard properties usually assumed to be fulfilled in order to prove theoretical or numerical results. Numerical procedures for this sort of non-standard conservation laws (NSCL) are not yet available in the literature. An abstract theorem for the convergence of discretisation procedures in case of problems whose solutions are uniquely determined by inequalities will be presented. First steps towards numerical methods for solving NSCL-problems could be successfully done by means of this general theory and will be presented in this paper.