Finite volume method
= Finite volume method
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A finite volume method evolves cell integrals or cell averages by differences of shared interface <numerical fluxes>. For a <scalar conservation law>, $U_j^{n+1}=U_j^n-(k/d)(F_{j+1/2}-F_{j-1/2})$. Sharing the same flux between neighboring cells makes conservation follow by telescoping.