Robust a posteriori error estimators with error-dominated oscillation for the reaction-diffusion equation

TL;DR

This paper develops a robust a posteriori error estimator for the reaction-diffusion equation that provides reliable bounds independent of the reaction-diffusion ratio, improving error assessment in numerical solutions.

Contribution

It introduces a new oscillation concept that, combined with the estimator, yields bounds unaffected by the reaction-diffusion ratio, advancing error estimation techniques.

Findings

Provides global upper and local lower error bounds

Constants are independent of the reaction-diffusion ratio

Oscillation is bounded by the error in a robust manner

Abstract

We apply the recent approach of C. Kreuzer and A. Veeser to derive a robust a posteriori error estimator for the reaction-diffusion equation. The estimator together with the corresponding oscillation yields global upper and local lower bounds for the error in the energy norm, and the involved constants do not depend on the ratio of reaction to diffusion. In particular the new oscillation is also bounded by the error in a robust way.