Space-time error control using a partition-of-unity dual-weighted residual method applied to low mach number combustion

TL;DR

This paper introduces a space-time goal-oriented error estimation method using a partition-of-unity dual-weighted residual approach, applied to low Mach number combustion, with numerical tests analyzing convergence and estimator effectiveness.

Contribution

It presents a novel space-time error estimation technique for combustion simulations using a dual-weighted residual method with partition-of-unity, enhancing accuracy and efficiency.

Findings

Effective error estimation demonstrated in numerical tests

Convergence orders consistent with theoretical predictions

Estimator accuracy varies with interpolation variants

Abstract

In this work, a space-time scheme for goal-oriented a posteriori error estimation is proposed. The error estimator is evaluated using a partition-of-unity dual-weighted residual method. As application, a low mach number combustion equation is considered. In some numerical tests, different interpolation variants are investigated, while observing convergence orders and effectivity indices between true errors (obtained on a sufficiently refined mesh) and the error estimator.