Error analysis in unconditionally stable coarsening algorithms

TL;DR

This paper quantitatively analyzes the accuracy of unconditionally stable coarsening algorithms by calculating Fourier space multi-step errors, highlighting the importance of correction terms in the analytic time step for improved precision.

Contribution

It introduces a method to compute the Fourier space multi-step error and clarifies the role of correction terms in the accuracy of unconditionally stable coarsening algorithms.

Findings

Error correction term significantly improves accuracy

Explicit distinction between analytic and algorithmic time is crucial

Quantitative error analysis enhances understanding of algorithm performance

Abstract

In order to quantitatively study the accuracy of the unconditionally stable coarsening algorithms, we calculate the Fourier space multi step error on the order parameter field by explicitly distinguishing the analytic time $\tau$ and the algorithmic time $t$. The calculation determines the error in the order parameter and the scaled correlations. This error contributes a correction term in the analytic time step, which is crucial in understanding the accuracy in unconditionally stable coarsening algorithms.