On Estimation of Discretization Error Norm via Ensemble of Approximate Solutions

TL;DR

This paper proposes a method to estimate the discretization error norm by using an ensemble of solutions from different solvers, validated through numerical tests on supersonic flows governed by Euler equations.

Contribution

It introduces a novel ensemble-based approach for discretization error estimation that distinguishes between accurate and inaccurate solutions.

Findings

Ensemble solutions provide an upper bound for the discretization error norm.

Clustering solutions into accurate and inaccurate groups improves estimation accuracy.

Numerical tests confirm the method's feasibility for supersonic flow simulations.

Abstract

The issue of single-grid discretization error estimator, operating in the postprocessor mode, is addressed in the paper. An ensemble of numerical solutions, obtained using solvers of different accuracy, is shown to provide an upper estimate for the norm of the discretization error. Numerical tests for the supersonic flows, governed by two dimensional Euler equations, confirm the feasibility for the norm estimation, if the ensemble of numerical solutions is separated into clusters of accurate and inaccurate solutions.