A posteriori estimates for errors of functionals on finite volume approximations to solutions of elliptic boundary value problems

TL;DR

This paper extends dual-weighted residual a posteriori error estimation methods to node-centered finite volume discretizations of elliptic boundary value problems, enabling error estimation for various error sources with respect to specific output functionals.

Contribution

It introduces a novel extension of a posteriori error estimation techniques to finite volume methods, including upwind schemes, for elliptic problems.

Findings

Effective estimation of discretization errors in finite volume methods.

Ability to estimate modeling errors alongside discretization errors.

Application to various output functionals.

Abstract

This article describes the extension of recent methods for a posteriori error estimation such as dual-weighted residual methods to node-centered finite volume discretizations of second order elliptic boundary value problems including upwind discretizations. It is shown how different sources of errors, in particular modeling errors and discretization errors, can be estimated with respect to a user-defined output functional.