= Fourth-order correction of the nine-point Poisson stencil
For a smooth solution of $\Delta u=f$, the corrected formula $\Gamma_9u=h^2f+(h^2/12)\Gamma_5f$ has unscaled residual $O(h^6)$ and normalized <local truncation error> $O(h^4)$. The inverse interior matrix has Euclidean <operator norm> $O(h^{-2})$; on $O(h^{-2})$ grid points this gives unweighted Euclidean nodal error $O(h^3)$. Uniform derivatives up to the boundary are required for a grid-independent remainder bound.
Back to article page
