centered_4th_uniform_latlon

Family: finite_difference
Grid family: latlon
Kind: scheme
Accuracy: O(h^4)
Applies to: grad($u), dim=$k
Rule file: discretizations/finite_difference/centered_4th_uniform_latlon.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 grad on the pattern grad($u), dim=$k for grid family latlon.

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):

−8/(12·R·cos_lat·dlon)·index($u, lat, lon + −1) + 8/(12·R·cos_lat·dlon)·index($u, lat, lon + 1)

Source: discretizations/finite_difference/centered_4th_uniform_latlon.json.