Goal-oriented A Posteriori Error Estimation for Finite Volume Methods

TL;DR

This paper introduces a general framework for goal-oriented a posteriori error estimation tailored for finite volume methods, enabling effective adaptive mesh refinement without relying on finite element recasting.

Contribution

The framework directly derives error estimators from finite volume discretized equations, applicable to any finite volume method, and addresses well-posedness of primal and adjoint problems.

Findings

Numerical results validate the accuracy of the error estimates.

The approach effectively guides adaptive mesh refinement.

Framework applicable to various finite volume schemes.

Abstract

A general framework for goal-oriented a posteriori error estimation for finite volume methods is presented. The framework does not rely on recasting finite volume methods as special cases of finite element methods, but instead directly determines error estimators from the discretized finite volume equations. Thus, the framework can be ap- plied to arbitrary finite volume methods. It also provides the proper functional settings to address well-posedness issues for the primal and adjoint problems. Numerical results are presented to illustrate the validity and effectiveness of the a posteriori error estimates and their applicability to adaptive mesh refinement.