Semi-Lagrangian Difference Approximations for Different Conservation Laws

Abstract

The paper demonstrates different ways of using the semi-Lagrangian approximation depending on the fulfillment of conservation laws. A one-dimensional parabolic equation is taken as a simple methodological example. For this equation, the principles of constructing discrete analogues are demonstrated in the context of two different conservation laws. It is important that different conservation laws yield difference problems of different types as well as different ways to justify their stability and convergence.