A Recovery-Based Error Indicator for Finite Difference Methods
Abstract
A novel recovery-based error indicator for high-order Finite Difference Methods, based on post-processing of the Finite Difference values is presented. The values obtained on the Finite Difference grid are interpolated into a suitable polynomial Finite Element space. A recovery-based error indicator, with the polynomial-preserving property, is then applied to estimate the gradient error. The performance and accuracy of the proposed error indicator are demonstrated through several numerical experiments, including the two-dimensional Poisson problem solved using second- and fourth-order finite difference schemes. Additional experiments are conducted on elliptic problems with discontinuous coefficients, as well as on the two and three-dimensional wave equation in homogeneous media with second- and fourth-order finite differences, and in heterogeneous media with second-order finite differences.
Cite
@article{arxiv.2601.11308,
title = {A Recovery-Based Error Indicator for Finite Difference Methods},
author = {Ferhat Sindy and Annalisa Buffa and Marco Picasso},
journal= {arXiv preprint arXiv:2601.11308},
year = {2026}
}