... by¹

The standard seven-point diffusion operator does not account for a flux source term, $\mbox{$\stackrel{^{\mathstrut}\smash{\longrightarrow}}{J}$}$, so that is omitted from the current discussion.

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... faces.²

In general, for multiple dimensions the scheme has $\left(\vphantom{ \left( n_d +1 \right) n_c + n_b/2 }\right.$$\left(\vphantom{ n_d +1 }\right.$n_d + 1$\left.\vphantom{ n_d +1 }\right)$n_c + n_b/2$\left.\vphantom{ \left( n_d +1 \right) n_c + n_b/2 }\right)$ unknowns, where n_d is the number of dimensions.

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... quartic³

The method is exact for linear solutions, so no improvement is achieved by refining the mesh in that situation.

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