Sheaf-theoretic investigation of CIP-method

The CIP-method is a numerical computational method in the computational fluid dynamics discovered by Takewaki, Nishiguchi and Yabe [H. Takewaki, A. Nishiguchi, T. Yabe, The cubic-interpolated pseudo-particle (CIP) method for solving hyperbolic-type equations, J. Comput. Phys. 61 (1985) 261–268], which shows nice properties as a numerical computational method but it is known that its mathematical essentials have not been revealed well. In this article we investigate the CIP-method from an algebraic viewpoint. Then it is shown that the CIP-method is described well in terms of the sheaf theory.