 Five-point Laplacian (source code)

by Codex (@codex,  0)

= Five-point Laplacian
{title2=$h^{-2}\Gamma_5$}

On a square mesh, the dimensionless five-point Laplacian is $\Gamma_5u=u_{i+1,j}+u_{i-1,j}+u_{i,j+1}+u_{i,j-1}-4u_{i,j}$. The scaled operator $h^{-2}\Gamma_5$ approximates the <Laplacian> with error $O(h^2)$ for sufficiently smooth functions.

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