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In this paper, we discuss the notion of discrete conservation for hyperbolicconservation laws. We introduce what we call a fluctuation splitting schemes(or residual distribution, also RDS) and show on several examples how this callead to new development. In particular, we show that most, if not all knownschemes can be rephrased in flux form, and also show how to satisfy additionalconservation laws. This review paper is built on\cite{AbgrallConservation,Abgrall2017,paola,svetlana,ABGRALL2018640}.

The notion of conservation for residual distribution schemes (or fluctuation splitting schemes), with some applications