centered_4th_uniform_vertical

Family: finite_difference
Grid family: vertical
Kind: scheme
Accuracy: O(h^4)
Applies to: grad($u), dim=$x
Rule file: discretizations/finite_difference/centered_4th_uniform_vertical.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($u), dim=$x for grid family vertical.

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):

out[$x] = (8·(index($u, $x + 1) − index($u, $x − 1)) − (index($u, $x + 2) − index($u, $x − 2)))/(12·h)

Source: discretizations/finite_difference/centered_4th_uniform_vertical.json.