gpd-numerical-convergence

Numerical convergence validation systematically refines discretization parameters like grid size and time step to expose discretization errors and quantify uncertainty. This process applies Richardson extrapolation to estimate true values and confirm results are trustworthy.

Richardson extrapolation is an error estimation technique applied during convergence testing to project the true solution from a series of refined discretization parameters. It builds an error budget to estimate exact values and quantify numerical uncertainty.

Perform convergence testing by systematically refining phase-appropriate computations such as basis size for PDEs or sample count for Monte Carlo simulations. The workflow includes benchmark validation against analytical results and conservation-law checks.

Yes, convergence validation applies to ODEs, PDEs, eigenvalue problems, and Monte Carlo simulations. It targets phase-appropriate computations by refining grid sizes, time steps, basis sizes, and sample counts to ensure stability and accuracy.

The best way involves a rigorous validation workflow combining stability analysis and conservation checks alongside convergence testing. This approach benchmarks results against analytical data to ensure numerical physics computations remain stable and physically accurate.

A structured validation report requires running a comprehensive workflow covering error estimation, stability analysis, and benchmarking. Completing this process automatically generates a NUMERICAL-VALIDATION.md report detailing your convergence studies and uncertainty quantification.