laplacian_2nd_uniform_cartesian

Family: finite_difference
Grid family: cartesian
Kind: scheme
Accuracy: O(dx^2)
Applies to: laplacian($u)
Rule file: discretizations/finite_difference/laplacian_2nd_uniform_cartesian.json

This page is auto-generated from the rule's JSON by tools/render_doc_plots.py. The discrete operator below is pretty-printed directly from the rule's replacement AST using EarthSciSerialization (earthsci_toolkit). Rules with a hand-authored page carry richer prose plus stencil and convergence diagrams; see the curated entries linked from the rule index.

Pattern

Matches the §4.2 operator laplacian on the pattern laplacian($u) for grid family cartesian.

Discrete operator

Pretty-printed from the rule’s replacement AST ($-prefixed names are pattern variables bound by applies_to; grid metrics such as dx/dz are resolved by the grid):

1/(dx·dx)·index($u, i + −1, j) + −2/(dx·dx)·index($u, i, j)

Source: discretizations/finite_difference/laplacian_2nd_uniform_cartesian.json.