Robust a-posteriori error estimates for weak Galerkin method for the convection-diffusion problem

TL;DR

This paper develops a robust a posteriori error estimator for the weak Galerkin finite element method applied to convection-diffusion problems, providing reliable error bounds in convection-dominated regimes.

Contribution

It introduces a new error estimator that remains effective regardless of the diffusion coefficient, improving reliability in convection-dominated scenarios.

Findings

The estimator provides both upper and lower error bounds.

Numerical experiments confirm the estimator's robustness.

Performance is consistent across different convection-diffusion regimes.

Abstract

We present a robust a posteriori error estimator for the weak Galerkin finite element method applied to stationary convection-diffusion equations in the convection-dominated regime. The estimator provides global upper and lower bounds of the error %measured in a suitable norm and is robust in the sense that upper and lower bounds are uniformly bounded with respect to the diffusion coefficient. Results of the numerical experiments are presented to illustrate the performance of the error estimator.