gpd-numerical-convergence

Numerical grid refinement studies are validated by capturing observable changes across discretization parameters and estimating convergence orders. This Skill automates parameter discovery, applies systematic refinement, and performs Richardson extrapolation to produce structured reports with error budgets and stability checks.

Richardson extrapolation is a numerical validation technique applied during convergence studies to combine results from different discretization levels and estimate the exact solution. It is used when observable changes are captured across systematic grid refinements to improve accuracy estimates.

An error budget for numerical simulations is built by identifying computations and accuracy-controlling parameters like tolerances, then applying structured refinement studies. The resulting report captures observable changes, estimates convergence orders, and quantifies discretization artifacts.

No specific simulation frameworks or dependencies are required. The workflow initializes by specifying a target phase or file path to discover computations and controlling parameters, making it adaptable to various numerical environments.

The best way to check numerical stability is to perform automated discovery of computations and controlling parameters, then apply systematic refinement across basis size and tolerances. This captures observable changes and generates reproducible results with comprehensive stability checks.

Numerical solutions change during grid size refinement due to discretization artifacts. You quantify this by applying systematic refinement, capturing observable changes, estimating convergence orders, and generating a structured report with an error budget to demonstrate independence from discretization.