An a posteriori error estimate of the outer normal derivative using dual weights

TL;DR

This paper develops a residual-based a posteriori error estimate for the outer normal flux in diffusion problems, enabling more efficient mesh refinement by focusing on boundary regions through dual-weighted analysis.

Contribution

It introduces a novel a posteriori error estimate for the boundary flux using dual weights, improving mesh efficiency in diffusion problem approximations.

Findings

Error indicators near the boundary are of lower order, allowing targeted mesh refinement.

Numerical examples confirm the effectiveness of the boundary-focused error estimates.

Abstract

We derive a residual based a-posteriori error estimate for the outer normal flux of approximations to {the diffusion problem with variable coefficient}. By analyzing the solution of the adjoint problem, we show that error indicators in the bulk may be defined to be of higher order than those close to the boundary, which lead to more economic meshes. The theory is illustrated with some numerical examples.